Eulertype Diagrams and the Quantification of the Predicate
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190629
Abstract:
Logicians have often suggested that the use of Eulertype diagrams has influenced the idea of the quantification of the predicate. This is mainly due to the fact that Eulertype diagrams display more information than is required in traditional syllogistics. The paper supports this argument and extends it by a further step: Eulertype diagrams not only illustrate the quantification of the predicate, but also solve problems of traditional proof theory, which prevented an overall quantification of the predicate. Thus, Eulertype diagrams can be called the natural basis of syllogistic reasoning and can even go beyond. In the paper, these arguments are presented in connection with the book Nucleus Logicae Weisaniae by Johann Christian Lange from 1712. Word Count:
Rank  Word  Count 
0  diagrams  4 
Excerpts:
...often suggested that the use of eulertype diagrams has influenced the idea of the quantification ...
...mainly due to the fact that eulertype diagrams display more information than is required in ...
...extends it by a further step eulertype diagrams not only illustrate the quantification of the ...
...overall quantification of the predicate thus eulertype diagrams can be called the natural basis of ...

1  eulertype  4 
Excerpts:
...have often suggested that the use of eulertype diagrams has influenced the idea of the ...
...is mainly due to the fact that eulertype diagrams display more information than is required ...
...and extends it by a further step eulertype diagrams not only illustrate the quantification of ...
...an overall quantification of the predicate thus eulertype diagrams can be called the natural basis ...

2  quantification  3 
Excerpts:
...diagrams has influenced the idea of the quantification of the predicate this is mainly due ...
...step eulertype diagrams not only illustrate the quantification of the predicate but also solve problems ...
...traditional proof theory which prevented an overall quantification of the predicate thus eulertype diagrams can ...

3  predicate  3 
Excerpts:
...the idea of the quantification of the predicate this is mainly due to the fact ...
...not only illustrate the quantification of the predicate but also solve problems of traditional proof ...
...which prevented an overall quantification of the predicate thus eulertype diagrams can be called the ...

4  traditional  2 
Excerpts:
...display more information than is required in traditional syllogistics the paper supports this argument and ...
...the predicate but also solve problems of traditional proof theory which prevented an overall quantification ...

5  syllogistic  1 
Excerpts:
...can be called the natural basis of syllogistic reasoning and can even go beyond in ...

6  go  1 
Excerpts:
...basis of syllogistic reasoning and can even go beyond in the paper these arguments are ...

7  reasoning  1 
Excerpts:
...be called the natural basis of syllogistic reasoning and can even go beyond in the ...

8  basis  1 
Excerpts:
...eulertype diagrams can be called the natural basis of syllogistic reasoning and can even go ...

9  even  1 
Excerpts:
...natural basis of syllogistic reasoning and can even go beyond in the paper these arguments ...

Classical Logic and the Strict Tolerant Hierarchy
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190621
Abstract:
In their recent article A Hierarchy of Classical and Paraconsistent Logics', Eduardo Barrio, Federico Pailos and Damien Szmuc (BPS hereafter) present novel and striking results about metainferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of nonclassical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a logic which agrees with classical logic on tautologies, inferences, metainferences, metametainferences, metameta...(n  3 times)metainferences, but that disagrees with classical logic on n + 1metainferences. They suggest that this shows that classical logic can only be characterized by defining its valid inferences at all orders. In this article, I invoke some simple symmetric generalizations of BPS's results to show that the problem is worse than they suggest, since in fact there are logics that agree with classical logic on inferential validity to all orders but still intuitively differ from it. I then discuss the relevance of these results for truth theory and the classification problem. Word Count:
Rank  Word  Count 
0  classical  6 
Excerpts:
...in their recent article a hierarchy of classical and paraconsistent logics eduardo barrio federico pailos ...
...interesting relations to various familiar logics including classical logic one such result is that for ...
...there is a logic which agrees with classical logic on tautologies inferences metainferences metametainferences metametan ...
... 3 timesmetainferences but that disagrees with classical logic on n + 1metainferences they suggest ...
...1metainferences they suggest that this shows that classical logic can only be characterized by defining ...
...fact there are logics that agree with classical logic on inferential validity to all orders ...

1  logic  6 
Excerpts:
...relations to various familiar logics including classical logic one such result is that for each ...
...each natural number n there is a logic which agrees with classical logic on tautologies ...
...is a logic which agrees with classical logic on tautologies inferences metainferences metametainferences metametan ...
...3 timesmetainferences but that disagrees with classical logic on n + 1metainferences they suggest that ...
...they suggest that this shows that classical logic can only be characterized by defining its ...
...there are logics that agree with classical logic on inferential validity to all orders but ...

2  logics  5 
Excerpts:
...article a hierarchy of classical and paraconsistent logics eduardo barrio federico pailos and damien szmuc ...
...about metainferential validity in various three valued logics in the process they have thrown open ...
...to a hitherto unrecognized domain of nonclassical logics with surprising intrinsic properties as well as ...
...subtle and interesting relations to various familiar logics including classical logic one such result is ...
...they suggest since in fact there are logics that agree with classical logic on inferential ...

3  results  3 
Excerpts:
...szmuc bps hereafter present novel and striking results about metainferential validity in various three valued ...
...invoke some simple symmetric generalizations of bpss results to show that the problem is worse ...
...i then discuss the relevance of these results for truth theory and the classification problem ...

4  various  2 
Excerpts:
...and striking results about metainferential validity in various three valued logics in the process they ...
...well as subtle and interesting relations to various familiar logics including classical logic one such ...

5  n  2 
Excerpts:
...result is that for each natural number n there is a logic which agrees with ...
...but that disagrees with classical logic on n + 1metainferences they suggest that this shows ...

6  validity  2 
Excerpts:
...present novel and striking results about metainferential validity in various three valued logics in the ...
...that agree with classical logic on inferential validity to all orders but still intuitively differ ...

7  orders  2 
Excerpts:
...by defining its valid inferences at all orders in this article i invoke some simple ...
...classical logic on inferential validity to all orders but still intuitively differ from it i ...

8  article  2 
Excerpts:
... in their recent article a hierarchy of classical and paraconsistent logics ...
...valid inferences at all orders in this article i invoke some simple symmetric generalizations of ...

9  suggest  2 
Excerpts:
...classical logic on n + 1metainferences they suggest that this shows that classical logic can ...
...that the problem is worse than they suggest since in fact there are logics that ...

Free Choice Impossibility Results
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190618
Abstract:
Free Choice is the principle that possibly p or q implies and is implied by possibly p and possibly q. A variety of recent attempts to validate Free Choice rely on a nonclassical semantics for disjunction, where the meaning of p or q is not a set of possible worlds. This paper begins with a battery of impossibility results, showing that some kind of nonclassical semantics for disjunction is required in order to validate Free Choice. The paper then provides a positive account of Free Choice, by identifying a family of dynamic semantics for disjunction that can validate the inference. On all such theories, the meaning of p or q has two parts. First, p or q requires that our information is consistent with each of p and q. Second, p or q narrows down our information by eliminating some worlds. It turns out that this second component of or is well behaved: there is a strongest such meaning that p or q can express, consistent with validating Free Choice. The strongest such meaning is the classical one, on which p or q eliminates any world where both p and q are false. In this way, the classical meaning of disjunction turns out to be intimately related to the validity of Free Choice. Word Count:
Rank  Word  Count 
0  p  10 
Excerpts:
...free choice is the principle that possibly p or q implies and is implied by ...
...q implies and is implied by possibly p and possibly q a variety of recent ...
...semantics for disjunction where the meaning of p or q is not a set of ...
...on all such theories the meaning of p or q has two parts first p ...
...p or q has two parts first p or q requires that our information is ...
...our information is consistent with each of p and q second p or q narrows ...
...with each of p and q second p or q narrows down our information by ...
...there is a strongest such meaning that p or q can express consistent with validating ...
...meaning is the classical one on which p or q eliminates any world where both ...
...or q eliminates any world where both p and q are false in this way ...

1  q  10 
Excerpts:
...is the principle that possibly p or q implies and is implied by possibly p ...
...is implied by possibly p and possibly q a variety of recent attempts to validate ...
...disjunction where the meaning of p or q is not a set of possible worlds ...
...such theories the meaning of p or q has two parts first p or q ...
...q has two parts first p or q requires that our information is consistent with ...
...is consistent with each of p and q second p or q narrows down our ...
...of p and q second p or q narrows down our information by eliminating some ...
...a strongest such meaning that p or q can express consistent with validating free choice ...
...the classical one on which p or q eliminates any world where both p and ...
...eliminates any world where both p and q are false in this way the classical ...

2  free  6 
Excerpts:
... free choice is the principle that possibly p ...
...a variety of recent attempts to validate free choice rely on a nonclassical semantics for ...
...disjunction is required in order to validate free choice the paper then provides a positive ...
...paper then provides a positive account of free choice by identifying a family of dynamic ...
...or q can express consistent with validating free choice the strongest such meaning is the ...
...be intimately related to the validity of free choice ...

3  choice  6 
Excerpts:
... free choice is the principle that possibly p or ...
...variety of recent attempts to validate free choice rely on a nonclassical semantics for disjunction ...
...is required in order to validate free choice the paper then provides a positive account ...
...then provides a positive account of free choice by identifying a family of dynamic semantics ...
...q can express consistent with validating free choice the strongest such meaning is the classical ...
...intimately related to the validity of free choice ...

4  meaning  5 
Excerpts:
...a nonclassical semantics for disjunction where the meaning of p or q is not a ...
...the inference on all such theories the meaning of p or q has two parts ...
...well behaved there is a strongest such meaning that p or q can express consistent ...
...with validating free choice the strongest such meaning is the classical one on which p ...
...are false in this way the classical meaning of disjunction turns out to be intimately ...

5  disjunction  4 
Excerpts:
...choice rely on a nonclassical semantics for disjunction where the meaning of p or q ...
...that some kind of nonclassical semantics for disjunction is required in order to validate free ...
...identifying a family of dynamic semantics for disjunction that can validate the inference on all ...
...in this way the classical meaning of disjunction turns out to be intimately related to ...

6  possibly  3 
Excerpts:
... free choice is the principle that possibly p or q implies and is implied ...
...or q implies and is implied by possibly p and possibly q a variety of ...
...and is implied by possibly p and possibly q a variety of recent attempts to ...

7  validate  3 
Excerpts:
...q a variety of recent attempts to validate free choice rely on a nonclassical semantics ...
...for disjunction is required in order to validate free choice the paper then provides a ...
...of dynamic semantics for disjunction that can validate the inference on all such theories the ...

8  semantics  3 
Excerpts:
...validate free choice rely on a nonclassical semantics for disjunction where the meaning of p ...
...results showing that some kind of nonclassical semantics for disjunction is required in order to ...
...choice by identifying a family of dynamic semantics for disjunction that can validate the inference ...

9  nonclassical  2 
Excerpts:
...to validate free choice rely on a nonclassical semantics for disjunction where the meaning of ...
...impossibility results showing that some kind of nonclassical semantics for disjunction is required in order ...

An Accuracy Argument in Favor of Ranking Theory
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190610
Abstract:
Fitelson and McCarthy (2014) have proposed an accuracy measure for confidence orders which favors probability measures and DempsterShafer belief functions as accounts of degrees of belief and excludes ranking functions. Their accuracy measure only penalizes mistakes in confidence comparisons. We propose an alternative accuracy measure that also rewards correct confidence comparisons. Thus we conform to both of William James' maxims: Believe truth! Shun error!' We combine the two maxims, penalties and rewards, into one criterion that we call prioritized accuracy optimization (PAO). That is, PAO punishes wrong comparisons (preferring the false to the true) and rewards right comparisons (preferring the true to the false). And it requires to prioritize being right und avoiding to be wrong in a specific way. Thus PAO is both, a scoring rule and a decision rule. It turns out that precisely confidence orders representable by twosided ranking functions satisfy PAO. The point is not to argue that PAO is the better accuracy goal. The point is only that ranking theory can also be supported by accuracy considerations. Thus, those considerations by themselves cannot decide about rational formats for degrees of belief, but are part and parcel of an overall normative assessment of those formats. Word Count:
Rank  Word  Count 
0  accuracy  6 
Excerpts:
...fitelson and mccarthy 2014 have proposed an accuracy measure for confidence orders which favors probability ...
...of belief and excludes ranking functions their accuracy measure only penalizes mistakes in confidence comparisons ...
...in confidence comparisons we propose an alternative accuracy measure that also rewards correct confidence comparisons ...
...into one criterion that we call prioritized accuracy optimization pao that is pao punishes wrong ...
...to argue that pao is the better accuracy goal the point is only that ranking ...
...ranking theory can also be supported by accuracy considerations thus those considerations by themselves cannot ...

1  pao  5 
Excerpts:
...criterion that we call prioritized accuracy optimization pao that is pao punishes wrong comparisons preferring ...
...call prioritized accuracy optimization pao that is pao punishes wrong comparisons preferring the false to ...
...be wrong in a specific way thus pao is both a scoring rule and a ...
...orders representable by twosided ranking functions satisfy pao the point is not to argue that ...
...the point is not to argue that pao is the better accuracy goal the point ...

2  confidence  4 
Excerpts:
...2014 have proposed an accuracy measure for confidence orders which favors probability measures and dempstershafer ...
...their accuracy measure only penalizes mistakes in confidence comparisons we propose an alternative accuracy measure ...
...alternative accuracy measure that also rewards correct confidence comparisons thus we conform to both of ...
...decision rule it turns out that precisely confidence orders representable by twosided ranking functions satisfy ...

3  comparisons  4 
Excerpts:
...accuracy measure only penalizes mistakes in confidence comparisons we propose an alternative accuracy measure that ...
...accuracy measure that also rewards correct confidence comparisons thus we conform to both of william ...
...optimization pao that is pao punishes wrong comparisons preferring the false to the true and ...
...false to the true and rewards right comparisons preferring the true to the false and ...

4  functions  3 
Excerpts:
...which favors probability measures and dempstershafer belief functions as accounts of degrees of belief and ...
...of degrees of belief and excludes ranking functions their accuracy measure only penalizes mistakes in ...
...precisely confidence orders representable by twosided ranking functions satisfy pao the point is not to ...

5  rewards  3 
Excerpts:
...propose an alternative accuracy measure that also rewards correct confidence comparisons thus we conform to ...
...we combine the two maxims penalties and rewards into one criterion that we call prioritized ...
...preferring the false to the true and rewards right comparisons preferring the true to the ...

6  belief  3 
Excerpts:
...orders which favors probability measures and dempstershafer belief functions as accounts of degrees of belief ...
...belief functions as accounts of degrees of belief and excludes ranking functions their accuracy measure ...
...decide about rational formats for degrees of belief but are part and parcel of an ...

7  thus  3 
Excerpts:
...measure that also rewards correct confidence comparisons thus we conform to both of william james ...
...to be wrong in a specific way thus pao is both a scoring rule and ...
...can also be supported by accuracy considerations thus those considerations by themselves cannot decide about ...

8  ranking  3 
Excerpts:
...accounts of degrees of belief and excludes ranking functions their accuracy measure only penalizes mistakes ...
...that precisely confidence orders representable by twosided ranking functions satisfy pao the point is not ...
...accuracy goal the point is only that ranking theory can also be supported by accuracy ...

9  measure  3 
Excerpts:
...and mccarthy 2014 have proposed an accuracy measure for confidence orders which favors probability measures ...
...belief and excludes ranking functions their accuracy measure only penalizes mistakes in confidence comparisons we ...
...confidence comparisons we propose an alternative accuracy measure that also rewards correct confidence comparisons thus ...

Blame it on me
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190610
Abstract:
In this paper, we develop a formalisation of the main ideas of the work of Van de Poel on responsibility. Using the basic concepts through which the meanings of responsibility are defined, we construct a logic which enables to express sentences like individual i is accountable for Ï†', individual i is blameworthy for Ï†' and individual i has the obligation to see to it that Ï†'. This formalization clarifies the definitions of responsibility given by Van de Poel and highlights their differences and similarities. It also helps to assess the consistency of the formalisation of responsibility, not only by showing that definitions are not inconsistent, but also by providing a formal demonstration of the relation between three main meanings of responsibility (accountability, blameworthiness, and obligation). The formal account can be used to derive new properties of the concepts. With the help of the formalisation, we detect the occurrence of the problem of many hands (PMH) by defining a logical framework for reasoning about collective and individual responsibility. This logic extends the Coalition Epistemic Dynamic Logic (CEDL) by adding a notion of group knowledge (and generalize the definitions of individual responsibility to groups of agents), agent ability and knowing how to its semantics. Word Count:
Rank  Word  Count 
0  responsibility  7 
Excerpts:
...the work of van de poel on responsibility using the basic concepts through which the ...
...basic concepts through which the meanings of responsibility are defined we construct a logic which ...
...Ï† this formalization clarifies the definitions of responsibility given by van de poel and highlights ...
...assess the consistency of the formalisation of responsibility not only by showing that definitions are ...
...the relation between three main meanings of responsibility accountability blameworthiness and obligation the formal account ...
...framework for reasoning about collective and individual responsibility this logic extends the coalition epistemic dynamic ...
...knowledge and generalize the definitions of individual responsibility to groups of agents agent ability and ...

1  individual  5 
Excerpts:
...logic which enables to express sentences like individual i is accountable for Ï† individual i ...
...like individual i is accountable for Ï† individual i is blameworthy for Ï† and individual ...
...individual i is blameworthy for Ï† and individual i has the obligation to see to ...
...logical framework for reasoning about collective and individual responsibility this logic extends the coalition epistemic ...
...group knowledge and generalize the definitions of individual responsibility to groups of agents agent ability ...

2  logic  3 
Excerpts:
...of responsibility are defined we construct a logic which enables to express sentences like individual ...
...reasoning about collective and individual responsibility this logic extends the coalition epistemic dynamic logic cedl ...
...this logic extends the coalition epistemic dynamic logic cedl by adding a notion of group ...

3  definitions  3 
Excerpts:
...it that Ï† this formalization clarifies the definitions of responsibility given by van de poel ...
...of responsibility not only by showing that definitions are not inconsistent but also by providing ...
...notion of group knowledge and generalize the definitions of individual responsibility to groups of agents ...

4  Ï†  3 
Excerpts:
...sentences like individual i is accountable for Ï† individual i is blameworthy for Ï† and ...
...for Ï† individual i is blameworthy for Ï† and individual i has the obligation to ...
...the obligation to see to it that Ï† this formalization clarifies the definitions of responsibility ...

5  formalisation  3 
Excerpts:
... in this paper we develop a formalisation of the main ideas of the work ...
...helps to assess the consistency of the formalisation of responsibility not only by showing that ...
...the concepts with the help of the formalisation we detect the occurrence of the problem ...

6  meanings  2 
Excerpts:
...using the basic concepts through which the meanings of responsibility are defined we construct a ...
...demonstration of the relation between three main meanings of responsibility accountability blameworthiness and obligation the ...

7  main  2 
Excerpts:
...paper we develop a formalisation of the main ideas of the work of van de ...
...formal demonstration of the relation between three main meanings of responsibility accountability blameworthiness and obligation ...

8  van  2 
Excerpts:
...the main ideas of the work of van de poel on responsibility using the basic ...
...clarifies the definitions of responsibility given by van de poel and highlights their differences and ...

9  concepts  2 
Excerpts:
...de poel on responsibility using the basic concepts through which the meanings of responsibility are ...
...used to derive new properties of the concepts with the help of the formalisation we ...

Ungroundedness in Tarskian Languages
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
Several writers have assumed that when in Outline of a Theory of Truth' I wrote that the orthodox approach' “ that is, Tarski's account of the truth definition “ admits descending chains, I was relying on a simple compactness theorem argument, and that nonstandard models must result. However, I was actually relying on a paper on ˜pseudowellorderings' by Harrison (Transactions of the American Mathematical Society, 131, 527“543 1968). The descending hierarchy of languages I define is a standard model. Yablo's Paradox later emerged as a key to interpreting the result. Word Count:
Serious Actualism and HigherOrder Predication
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
Serious actualism is the prima facie plausible thesis that things couldn't have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga's argument (Plantinga Philosophical Studies, 44, 1“20 1983) for the claim that propositions do not ontologically depend on the things that they are about and in Williamson's argument (Williamson 2002) for the claim that he, Williamson, is necessarily something. Salmon (Philosophical Perspectives, 1, 49“108 1987) has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon's objection is based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon's objection. In addition, an argument for serious actualism based on Stephanou (Philosophical Review, 116(2), 219“250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higherorder modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. Word Count:
Completeness of SecondOrder Intuitionistic Propositional Logic with Respect to Phase Semantics for ProofTerms
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
Girard introduced phase semantics as a complete settheoretic semantics of linear logic, and Okada modified phasesemantic completeness proofs to obtain normalform theorems. On the basis of these works, Okada and Takemura reformulated Girard's phase semantics so that it became phase semantics for proofterms, i.e., lambdaterms. They formulated phase semantics for proofterms of Laird's dual affine/intuitionistic lambdacalculus and proved the normalform theorem for Laird's calculus via a completeness theorem. Their semantics was obtained by an application of computability predicates. In this paper, we first formulate phase semantics for proofterms of secondorder intuitionistic propositional logic by modifying TaitGirard's saturated sets method. Next, we prove the completeness theorem with respect to this semantics, which implies a strong normalization theorem. Word Count:
Rank  Word  Count 
0  semantics  8 
Excerpts:
... girard introduced phase semantics as a complete settheoretic semantics of linear ...
...introduced phase semantics as a complete settheoretic semantics of linear logic and okada modified phasesemantic ...
...works okada and takemura reformulated girards phase semantics so that it became phase semantics for ...
...phase semantics so that it became phase semantics for proofterms ie lambdaterms they formulated phase ...
...for proofterms ie lambdaterms they formulated phase semantics for proofterms of lairds dual affineintuitionistic lambdacalculus ...
...lairds calculus via a completeness theorem their semantics was obtained by an application of computability ...
...in this paper we first formulate phase semantics for proofterms of secondorder intuitionistic propositional logic ...
...the completeness theorem with respect to this semantics which implies a strong normalization theorem ...

1  phase  5 
Excerpts:
... girard introduced phase semantics as a complete settheoretic semantics of ...
...these works okada and takemura reformulated girards phase semantics so that it became phase semantics ...
...girards phase semantics so that it became phase semantics for proofterms ie lambdaterms they formulated ...
...semantics for proofterms ie lambdaterms they formulated phase semantics for proofterms of lairds dual affineintuitionistic ...
...predicates in this paper we first formulate phase semantics for proofterms of secondorder intuitionistic propositional ...

2  theorem  4 
Excerpts:
...dual affineintuitionistic lambdacalculus and proved the normalform theorem for lairds calculus via a completeness theorem ...
...theorem for lairds calculus via a completeness theorem their semantics was obtained by an application ...
...sets method next we prove the completeness theorem with respect to this semantics which implies ...
...this semantics which implies a strong normalization theorem ...

3  completeness  3 
Excerpts:
...of linear logic and okada modified phasesemantic completeness proofs to obtain normalform theorems on the ...
...normalform theorem for lairds calculus via a completeness theorem their semantics was obtained by an ...
...saturated sets method next we prove the completeness theorem with respect to this semantics which ...

4  proofterms  3 
Excerpts:
...so that it became phase semantics for proofterms ie lambdaterms they formulated phase semantics for ...
...ie lambdaterms they formulated phase semantics for proofterms of lairds dual affineintuitionistic lambdacalculus and proved ...
...paper we first formulate phase semantics for proofterms of secondorder intuitionistic propositional logic by modifying ...

5  normalform  2 
Excerpts:
...okada modified phasesemantic completeness proofs to obtain normalform theorems on the basis of these works ...
...lairds dual affineintuitionistic lambdacalculus and proved the normalform theorem for lairds calculus via a completeness ...

6  lairds  2 
Excerpts:
...they formulated phase semantics for proofterms of lairds dual affineintuitionistic lambdacalculus and proved the normalform ...
...lambdacalculus and proved the normalform theorem for lairds calculus via a completeness theorem their semantics ...

7  okada  2 
Excerpts:
...complete settheoretic semantics of linear logic and okada modified phasesemantic completeness proofs to obtain normalform ...
...theorems on the basis of these works okada and takemura reformulated girards phase semantics so ...

8  logic  2 
Excerpts:
...as a complete settheoretic semantics of linear logic and okada modified phasesemantic completeness proofs to ...
...semantics for proofterms of secondorder intuitionistic propositional logic by modifying taitgirards saturated sets method next ...

9  predicates  1 
Excerpts:
...was obtained by an application of computability predicates in this paper we first formulate phase ...

A Dynamic Solution to the Problem of Logical Omniscience
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
The traditional possibleworlds model of belief describes agents as ˜logically omniscient' in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of nonideal agents who'much like ordinary human beings'are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws of logic. In this paper, we argue that existing impossibleworlds models of belief fail to describe agents who are both logically nonomniscient and logically competent. To model such agents, we argue, we need to ˜dynamize' the impossibleworlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossibleworlds framework, and show that it successfully models agents who are both logically nonomniscient and logically competent. Word Count:
Implicit and Explicit Stances in Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
We identify a pervasive contrast between implicit and explicit stances in logical analysis and system design. Implicit systems change received meanings of logical constants and sometimes also the notion of consequence, while explicit systems conservatively extend classical systems with new vocabulary. We illustrate the contrast for intuitionistic and epistemic logic, then take it further to information dynamics, default reasoning, and other areas, to show its wide scope. This gives a working understanding of the contrast, though we stop short of a formal definition, and acknowledge limitations and borderline cases. Throughout we show how awareness of the two stances suggests new logical systems and new issues about translations between implicit and explicit systems, linking up with foundational concerns about identity of logical systems. But we also show how a practical facility with these complementary working styles has philosophical consequences, as it throws doubt on strong philosophical claims made by just taking one design stance and ignoring alternative ones. We will illustrate the latter benefit for the case of logical pluralism and hyperintensional semantics. Word Count:
Rank  Word  Count 
0  systems  6 
Excerpts:
...in logical analysis and system design implicit systems change received meanings of logical constants and ...
...also the notion of consequence while explicit systems conservatively extend classical systems with new vocabulary ...
...consequence while explicit systems conservatively extend classical systems with new vocabulary we illustrate the contrast ...
...of the two stances suggests new logical systems and new issues about translations between implicit ...
...issues about translations between implicit and explicit systems linking up with foundational concerns about identity ...
...with foundational concerns about identity of logical systems but we also show how a practical ...

1  logical  5 
Excerpts:
...contrast between implicit and explicit stances in logical analysis and system design implicit systems change ...
...design implicit systems change received meanings of logical constants and sometimes also the notion of ...
...awareness of the two stances suggests new logical systems and new issues about translations between ...
...up with foundational concerns about identity of logical systems but we also show how a ...
...the latter benefit for the case of logical pluralism and hyperintensional semantics ...

2  show  3 
Excerpts:
...dynamics default reasoning and other areas to show its wide scope this gives a working ...
...acknowledge limitations and borderline cases throughout we show how awareness of the two stances suggests ...
...identity of logical systems but we also show how a practical facility with these complementary ...

3  contrast  3 
Excerpts:
... we identify a pervasive contrast between implicit and explicit stances in logical ...
...systems with new vocabulary we illustrate the contrast for intuitionistic and epistemic logic then take ...
...this gives a working understanding of the contrast though we stop short of a formal ...

4  new  3 
Excerpts:
...explicit systems conservatively extend classical systems with new vocabulary we illustrate the contrast for intuitionistic ...
...how awareness of the two stances suggests new logical systems and new issues about translations ...
...two stances suggests new logical systems and new issues about translations between implicit and explicit ...

5  explicit  3 
Excerpts:
...identify a pervasive contrast between implicit and explicit stances in logical analysis and system design ...
...sometimes also the notion of consequence while explicit systems conservatively extend classical systems with new ...
...new issues about translations between implicit and explicit systems linking up with foundational concerns about ...

6  implicit  3 
Excerpts:
... we identify a pervasive contrast between implicit and explicit stances in logical analysis and ...
...stances in logical analysis and system design implicit systems change received meanings of logical constants ...
...systems and new issues about translations between implicit and explicit systems linking up with foundational ...

7  illustrate  2 
Excerpts:
...extend classical systems with new vocabulary we illustrate the contrast for intuitionistic and epistemic logic ...
...stance and ignoring alternative ones we will illustrate the latter benefit for the case of ...

8  philosophical  2 
Excerpts:
...facility with these complementary working styles has philosophical consequences as it throws doubt on strong ...
...consequences as it throws doubt on strong philosophical claims made by just taking one design ...

9  design  2 
Excerpts:
...explicit stances in logical analysis and system design implicit systems change received meanings of logical ...
...philosophical claims made by just taking one design stance and ignoring alternative ones we will ...

Basic Intuitionistic Conditional Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving (counterfactual) conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas' important classical system CK. I give ICK both worlds semantics and algebraic semantics, and prove that these are equivalent. I give a GÃ¶deltype embedding of ICK into CK (augmented with an S4 box connective) and a Glivenkotype embedding of CK into ICK. I axiomatize ICK and prove soundness, completeness, and decidability results. Finally, I discuss extending ICK. Word Count:
Rank  Word  Count 
0  ick  6 
Excerpts:
...thoroughly examining the basic intuitionistic conditional logic ick the intuitionistic counterpart of chellas important classical ...
...chellas important classical system ck i give ick both worlds semantics and algebraic semantics and ...
...equivalent i give a gÃ¶deltype embedding of ick into ck augmented with an s4 box ...
...and a glivenkotype embedding of ck into ick i axiomatize ick and prove soundness completeness ...
...embedding of ck into ick i axiomatize ick and prove soundness completeness and decidability results ...
...and decidability results finally i discuss extending ick ...

1  conditional  4 
Excerpts:
... conditional logics have traditionally been intended to formalize ...
...intuitively correct modes of reasoning involving counterfactual conditional expressions in natural language although conditional logics ...
...counterfactual conditional expressions in natural language although conditional logics have by now been thoroughly studied ...
...gap by thoroughly examining the basic intuitionistic conditional logic ick the intuitionistic counterpart of chellas ...

2  intuitionistic  3 
Excerpts:
...yet to be systematically examined in an intuitionistic context despite compelling philosophical and technical reasons ...
...this gap by thoroughly examining the basic intuitionistic conditional logic ick the intuitionistic counterpart of ...
...the basic intuitionistic conditional logic ick the intuitionistic counterpart of chellas important classical system ck ...

3  ck  3 
Excerpts:
...intuitionistic counterpart of chellas important classical system ck i give ick both worlds semantics and ...
...give a gÃ¶deltype embedding of ick into ck augmented with an s4 box connective and ...
...box connective and a glivenkotype embedding of ck into ick i axiomatize ick and prove ...

4  classical  2 
Excerpts:
...by now been thoroughly studied in a classical context they have yet to be systematically ...
...ick the intuitionistic counterpart of chellas important classical system ck i give ick both worlds ...

5  thoroughly  2 
Excerpts:
...although conditional logics have by now been thoroughly studied in a classical context they have ...
...so this paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ick ...

6  context  2 
Excerpts:
...now been thoroughly studied in a classical context they have yet to be systematically examined ...
...to be systematically examined in an intuitionistic context despite compelling philosophical and technical reasons to ...

7  prove  2 
Excerpts:
...both worlds semantics and algebraic semantics and prove that these are equivalent i give a ...
...ck into ick i axiomatize ick and prove soundness completeness and decidability results finally i ...

8  semantics  2 
Excerpts:
...system ck i give ick both worlds semantics and algebraic semantics and prove that these ...
...give ick both worlds semantics and algebraic semantics and prove that these are equivalent i ...

9  into  2 
Excerpts:
...i give a gÃ¶deltype embedding of ick into ck augmented with an s4 box connective ...
...connective and a glivenkotype embedding of ck into ick i axiomatize ick and prove soundness ...

Modal Expansionism
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
There are various wellknown paradoxes of modal recombination. This paper offers a solution to a variety of such paradoxes in the form of a new conception of metaphysical modality. On the proposed conception, metaphysical modality exhibits a type of indefinite extensibility. Indeed, for any objective modality there will always be some further, broader objective modality; in other terms, modal space will always be open to expansion. Word Count:
Rank  Word  Count 
0  modality  4 
Excerpts:
...form of a new conception of metaphysical modality on the proposed conception metaphysical modality exhibits ...
...metaphysical modality on the proposed conception metaphysical modality exhibits a type of indefinite extensibility indeed ...
...of indefinite extensibility indeed for any objective modality there will always be some further broader ...
...will always be some further broader objective modality in other terms modal space will always ...

1  always  2 
Excerpts:
...indeed for any objective modality there will always be some further broader objective modality in ...
...modality in other terms modal space will always be open to expansion ...

2  metaphysical  2 
Excerpts:
...the form of a new conception of metaphysical modality on the proposed conception metaphysical modality ...
...of metaphysical modality on the proposed conception metaphysical modality exhibits a type of indefinite extensibility ...

3  will  2 
Excerpts:
...extensibility indeed for any objective modality there will always be some further broader objective modality ...
...objective modality in other terms modal space will always be open to expansion ...

4  objective  2 
Excerpts:
...type of indefinite extensibility indeed for any objective modality there will always be some further ...
...there will always be some further broader objective modality in other terms modal space will ...

5  paradoxes  2 
Excerpts:
... there are various wellknown paradoxes of modal recombination this paper offers a ...
...a solution to a variety of such paradoxes in the form of a new conception ...

6  modal  2 
Excerpts:
... there are various wellknown paradoxes of modal recombination this paper offers a solution to ...
...further broader objective modality in other terms modal space will always be open to expansion ...

7  conception  2 
Excerpts:
...paradoxes in the form of a new conception of metaphysical modality on the proposed conception ...
...conception of metaphysical modality on the proposed conception metaphysical modality exhibits a type of indefinite ...

8  any  1 
Excerpts:
...a type of indefinite extensibility indeed for any objective modality there will always be some ...

9  broader  1 
Excerpts:
...modality there will always be some further broader objective modality in other terms modal space ...

Revision Without Revision Sequences: SelfReferential Truth
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190601
Abstract:
The model of selfreferential truth presented in this paper, named Revisiontheoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap's Revision Theory of Truth into the formal framework of Kripkean fixedpoint semantics. In Kripkestyle theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I want to do something similar replacing the Kripkean sets of grounded true sentences with revisiontheoretic sets of stable true sentences. This can be done by defining a monotone operator through a variant of van Fraassen's supervaluation scheme which is simply based on Ï‰length iterations of the Tarskian operator. Clearly, all virtues of Kripkestyle theories are preserved, and we can also prove that the resulting set of grounded' true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes. Word Count:
Rank  Word  Count 
0  true  6 
Excerpts:
...kripkestyle theories the final set of grounded true sentences can be reached from below along ...
...strictly increasing sequence of sets of grounded true sentences in this sense each stage of ...
...similar replacing the kripkean sets of grounded true sentences with revisiontheoretic sets of stable true ...
...true sentences with revisiontheoretic sets of stable true sentences this can be done by defining ...
...prove that the resulting set of grounded true sentences shares some nice features with the ...
...nice features with the sets of stable true sentences which are provided by the usual ...

1  sentences  6 
Excerpts:
...theories the final set of grounded true sentences can be reached from below along a ...
...increasing sequence of sets of grounded true sentences in this sense each stage of the ...
...replacing the kripkean sets of grounded true sentences with revisiontheoretic sets of stable true sentences ...
...sentences with revisiontheoretic sets of stable true sentences this can be done by defining a ...
...that the resulting set of grounded true sentences shares some nice features with the sets ...
...features with the sets of stable true sentences which are provided by the usual ways ...

2  sets  4 
Excerpts:
...below along a strictly increasing sequence of sets of grounded true sentences in this sense ...
...to do something similar replacing the kripkean sets of grounded true sentences with revisiontheoretic sets ...
...sets of grounded true sentences with revisiontheoretic sets of stable true sentences this can be ...
...sentences shares some nice features with the sets of stable true sentences which are provided ...

3  revision  4 
Excerpts:
...the philosophical insights of gupta and belnaps revision theory of truth into the formal framework ...
...provided by the usual ways of formalising revision what is expected is that a clearer ...
...be associated to this way of doing revision hopefully a content directly linked with the ...
...directly linked with the insights underlying finite revision processes ...

4  grounded  4 
Excerpts:
...in kripkestyle theories the final set of grounded true sentences can be reached from below ...
...a strictly increasing sequence of sets of grounded true sentences in this sense each stage ...
...something similar replacing the kripkean sets of grounded true sentences with revisiontheoretic sets of stable ...
...also prove that the resulting set of grounded true sentences shares some nice features with ...

5  set  2 
Excerpts:
...fixedpoint semantics in kripkestyle theories the final set of grounded true sentences can be reached ...
...we can also prove that the resulting set of grounded true sentences shares some nice ...

6  stable  2 
Excerpts:
...grounded true sentences with revisiontheoretic sets of stable true sentences this can be done by ...
...some nice features with the sets of stable true sentences which are provided by the ...

7  revisiontheoretic  2 
Excerpts:
...selfreferential truth presented in this paper named revisiontheoretic supervaluation aims to incorporate the philosophical insights ...
...kripkean sets of grounded true sentences with revisiontheoretic sets of stable true sentences this can ...

8  truth  2 
Excerpts:
... the model of selfreferential truth presented in this paper named revisiontheoretic supervaluation ...
...of gupta and belnaps revision theory of truth into the formal framework of kripkean fixedpoint ...

9  content  2 
Excerpts:
...is expected is that a clearer philosophical content could be associated to this way of ...
...this way of doing revision hopefully a content directly linked with the insights underlying finite ...

Intensional Protocols for Dynamic Epistemic Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190528
Abstract:
In dynamical multiagent systems, agents are controlled by protocols. In choosing a class of formal protocols, an implicit choice is made concerning the types of agents, actions and dynamics representable. This paper investigates one such choice: An intensional protocol class for agent control in dynamic epistemic logic (DEL), called ˜DEL dynamical systems'. After illustrating how such protocols may be used in formalizing and analyzing information dynamics, the types of epistemic temporal models that they may generate are characterized. This facilitates a formal comparison with the only other formal protocol framework in dynamic epistemic logic, namely the extensional ˜DEL protocols'. The paper concludes with a conceptual comparison, highlighting modeling tasks where DEL dynamical systems are natural. Word Count:
Explicating Logical Independence
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190525
Abstract:
Accounts of (complete) logical independence which coincide when applied in the case of classical logic diverge elsewhere, raising the question of what a satisfactory allpurpose account of logical independence might look like. ˜Allpurpose' here means: working satisfactorily as applied across different logics, taken as consequence relations. Principal candidate characterizations of independence relative to a consequence relation are (i) that there the consequence relation concerned is determined by (= sound and complete w.r.t.) only by classes of (bivalent) valuations providing for all possible truthvalue combinations for the formulas whose independence is at issue, and (ii) that the consequence relation ˜says' nothing special about how those formulas are related that it does not say about arbitrary formulas. (The latter approach, we associate with de Jongh, though it is closely related to Marczewski's notion of general algebraic independence, as well as to the absence of nontrivial logical relations as conceived by Lemmon.) Each of these proposals returns counterintuitive verdicts in certain cases'the truthvalue inspired approach classifying certain cases one would like to describe as involving failures of independence as being cases of independence, and the de Jongh approach counting some intuitively independent pairs of formulas as not being independent after all. In final section, a modification of the latter approach is tentatively sketched to correct for these misclassifications. The attention is on conceptual clarification throughout, rather than the provision of technical results. Proofs, as well as further elaborations, are lodged in the ˜longer notes' in a finalÂ Appendix. Word Count:
Substitution contradiction, its resolution and the ChurchRosser Theorem in TIL
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190516
Abstract:
I present an analysis according to which the current state of the definition of substitution leads to a contradiction in the system of Transparent Intensional Logic (TIL). I entail the contradiction using only the basic definitions of TIL and standard results. I then analyse the roots of the contradiction and motivate the path I take in resolving the contradiction. I provide a new amended definition of collisionless substitution which blocks the contradiction in a nonad hoc way. I elaborate on the consequences of the amended definition, namely the invalidity of the ChurchRosser theorem (the socalled diamond property). I present a counterexample to the validity of the theorem in TIL with an amended definition of substitution. Word Count:
Rank  Word  Count 
0  contradiction  5 
Excerpts:
...the definition of substitution leads to a contradiction in the system of transparent intensional logic ...
...transparent intensional logic til i entail the contradiction using only the basic definitions of til ...
...i then analyse the roots of the contradiction and motivate the path i take in ...
...the path i take in resolving the contradiction i provide a new amended definition of ...
...definition of collisionless substitution which blocks the contradiction in a nonad hoc way i elaborate ...

1  definition  4 
Excerpts:
...to which the current state of the definition of substitution leads to a contradiction in ...
...the contradiction i provide a new amended definition of collisionless substitution which blocks the contradiction ...
...elaborate on the consequences of the amended definition namely the invalidity of the churchrosser theorem ...
...the theorem in til with an amended definition of substitution ...

2  substitution  3 
Excerpts:
...the current state of the definition of substitution leads to a contradiction in the system ...
...provide a new amended definition of collisionless substitution which blocks the contradiction in a nonad ...
...in til with an amended definition of substitution ...

3  amended  3 
Excerpts:
...resolving the contradiction i provide a new amended definition of collisionless substitution which blocks the ...
...i elaborate on the consequences of the amended definition namely the invalidity of the churchrosser ...
...of the theorem in til with an amended definition of substitution ...

4  til  3 
Excerpts:
...in the system of transparent intensional logic til i entail the contradiction using only the ...
...contradiction using only the basic definitions of til and standard results i then analyse the ...
...to the validity of the theorem in til with an amended definition of substitution ...

5  present  2 
Excerpts:
... i present an analysis according to which the current ...
...churchrosser theorem the socalled diamond property i present a counterexample to the validity of the ...

6  theorem  2 
Excerpts:
...definition namely the invalidity of the churchrosser theorem the socalled diamond property i present a ...
...a counterexample to the validity of the theorem in til with an amended definition of ...

7  way  1 
Excerpts:
...blocks the contradiction in a nonad hoc way i elaborate on the consequences of the ...

8  hoc  1 
Excerpts:
...which blocks the contradiction in a nonad hoc way i elaborate on the consequences of ...

9  nonad  1 
Excerpts:
...substitution which blocks the contradiction in a nonad hoc way i elaborate on the consequences ...

The logic of ground
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190515
Abstract:
I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ˜Guide to Ground.' This logic, I argue, generates many plausible principles which Fine's system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It's elegant, parsimonious and explanatorily powerful. Yet, so I suggest, adopting it has important consequences. First, it means we should think of ground as a type of identity. Second, it means we should reject much of Fine's logic of strict ground. I also show how the logic I develop connects to other systems in the literature. It is definitionally equivalent both to Angell's logic of analytic containment and to Correia's system G. Word Count:
Expectation Biases and Context Management with Negative Polar Questions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190507
Abstract:
This paper examines distinctive discourse properties of preposed negative yes/no questions (NPQs), such as Isn't Jane coming too?. Unlike with other yes/no questions, using an NPQ ˆ¼ p? invariably conveys a bias toward a particular answer, where the polarity of the bias is opposite of the polarity of the question: using the negative question ˆ¼ p? invariably expresses that the speaker previously expected the positive answer p to be correct. A prominent approach' what I call the contextmanagement approach, developed most extensively by Romero and Han (Linguistics and Philosophy, 27, 609658 2004)' attempts to capture speaker expectation biases by treating NPQs fundamentally as epistemic questions about the proper discourse status of a proposition. I raise challenges for existing contextmanaging accounts to provide more adequate formalizations of the posited contextmanaging content, its implementation in the compositional semantics and discourse dynamics, and its role in generating the observed biases. New data regarding discourse differences between NPQs and associated epistemic modal questions are introduced. I argue that we can capture the roles of NPQs in expressing speakers' states of mind and managing the discourse common ground without positing special contextmanaging operators or treating NPQs as questions directly about the context. I suggest that we treat the operator introduced with preposed negation as having an ordinary semantics of epistemic necessity, though lexically associated with a general kind of endorsing use observed with modal expressions. The expressive and contextmanaging roles of NPQs are explained in terms of a general kind of discourseoriented use of contextsensitive language. The distinctive expectation biases and discourse properties observed with NPQs are derived from the proposed semantics and a general principle of Discourse Relevance. Word Count:
On Hierarchical Propositions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190426
Abstract:
There is an apparent dilemma for hierarchical accounts of propositions, raised by Bruno Whittle (Journal of Philosophical Logic, 46, 215“231, 2017): either such accounts do not offer adequate treatment of connectives and quantifiers, or they eviscerate the logic. I discuss what a plausible hierarchical conception of propositions might amount to, and show that on that conception, Whittle's dilemma is not compelling. Thus, there are good reasons why proponents of hierarchical accounts of propositions (such as Russell, Church, or Kaplan) did not see the difficulty Whittle raises. Word Count:
Negation on the Australian Plan
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190422
Abstract:
We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusionexpressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a manyvalued semantics. We show that the Australian Plan has substantial advantages over the American Plan. Word Count:
Rank  Word  Count 
0  plan  5 
Excerpts:
... we present and defend the australian plan semantics for negation this is a comprehensive ...
...defuse a number of objections to this plan raised by supporters of the american plan ...
...plan raised by supporters of the american plan for negation in which negation is handled ...
...manyvalued semantics we show that the australian plan has substantial advantages over the american plan ...
...plan has substantial advantages over the american plan ...

1  negation  5 
Excerpts:
...and defend the australian plan semantics for negation this is a comprehensive account suitable for ...
...on two ideas the first is that negation is an exclusionexpressing device we utter negations ...
...second is that because incompatibility is modal negation is a modal operator as well it ...
...by supporters of the american plan for negation in which negation is handled via a ...
...the american plan for negation in which negation is handled via a manyvalued semantics we ...

2  over  2 
Excerpts:
...can then be modelled as a quantifier over points in frames restricted by accessibility relations ...
...that the australian plan has substantial advantages over the american plan ...

3  points  2 
Excerpts:
...then be modelled as a quantifier over points in frames restricted by accessibility relations representing ...
...relations representing compatibilities and incompatibilities between such points we defuse a number of objections to ...

4  american  2 
Excerpts:
...this plan raised by supporters of the american plan for negation in which negation is ...
...australian plan has substantial advantages over the american plan ...

5  incompatibilities  2 
Excerpts:
...exclusionexpressing device we utter negations to express incompatibilities the second is that because incompatibility is ...
...restricted by accessibility relations representing compatibilities and incompatibilities between such points we defuse a number ...

6  modal  2 
Excerpts:
...the second is that because incompatibility is modal negation is a modal operator as well ...
...because incompatibility is modal negation is a modal operator as well it can then be ...

7  australian  2 
Excerpts:
... we present and defend the australian plan semantics for negation this is a ...
...a manyvalued semantics we show that the australian plan has substantial advantages over the american ...

8  semantics  2 
Excerpts:
...we present and defend the australian plan semantics for negation this is a comprehensive account ...
...which negation is handled via a manyvalued semantics we show that the australian plan has ...

9  compatibilities  1 
Excerpts:
...in frames restricted by accessibility relations representing compatibilities and incompatibilities between such points we defuse ...

