Intuitionistic Nonnormal Modal Logics: A General Framework
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200328
Abstract:
We define a family of intuitionistic nonnormal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert axiomatisation and a cutfree sequent calculus, on its basis we also prove their decidability. We then define a semantic characterisation of our logics in terms of neighbourhood models containing two distinct neighbourhood functions corresponding to the two modalities. Our semantic framework captures modularly not only our systems but also already known intuitionistic nonnormal modal logics such as Constructive K (CK) and the propositional fragment of Wijesekera's Constructive Concurrent Dynamic Logic. Word Count:
Rank  Word  Count 
0  logics  7 
Excerpts:
...define a family of intuitionistic nonnormal modal logics they can be seen as intuitionistic counterparts ...
...of classical ones we first consider monomodal logics which contain only necessity or possibility we ...
...consider the more important case of bimodal logics which contain both modal operators in this ...
...obtain a lattice of 24 distinct bimodal logics for all logics we provide both a ...
...of 24 distinct bimodal logics for all logics we provide both a hilbert axiomatisation and ...
...then define a semantic characterisation of our logics in terms of neighbourhood models containing two ...
...but also already known intuitionistic nonnormal modal logics such as constructive k ck and the ...

1  define  3 
Excerpts:
... we define a family of intuitionistic nonnormal modal logics ...
...both modal operators in this case we define several interactions between necessity and possibility of ...
...we also prove their decidability we then define a semantic characterisation of our logics in ...

2  intuitionistic  3 
Excerpts:
... we define a family of intuitionistic nonnormal modal logics they can be seen ...
...modal logics they can be seen as intuitionistic counterparts of classical ones we first consider ...
...only our systems but also already known intuitionistic nonnormal modal logics such as constructive k ...

3  modal  3 
Excerpts:
...we define a family of intuitionistic nonnormal modal logics they can be seen as intuitionistic ...
...case of bimodal logics which contain both modal operators in this case we define several ...
...systems but also already known intuitionistic nonnormal modal logics such as constructive k ck and ...

4  only  2 
Excerpts:
...we first consider monomodal logics which contain only necessity or possibility we then consider the ...
...modalities our semantic framework captures modularly not only our systems but also already known intuitionistic ...

5  semantic  2 
Excerpts:
...prove their decidability we then define a semantic characterisation of our logics in terms of ...
...functions corresponding to the two modalities our semantic framework captures modularly not only our systems ...

6  neighbourhood  2 
Excerpts:
...characterisation of our logics in terms of neighbourhood models containing two distinct neighbourhood functions corresponding ...
...terms of neighbourhood models containing two distinct neighbourhood functions corresponding to the two modalities our ...

7  distinct  2 
Excerpts:
...we thereby obtain a lattice of 24 distinct bimodal logics for all logics we provide ...
...in terms of neighbourhood models containing two distinct neighbourhood functions corresponding to the two modalities ...

8  constructive  2 
Excerpts:
...known intuitionistic nonnormal modal logics such as constructive k ck and the propositional fragment of ...
...ck and the propositional fragment of wijesekeras constructive concurrent dynamic logic ...

9  bimodal  2 
Excerpts:
...then consider the more important case of bimodal logics which contain both modal operators in ...
...thereby obtain a lattice of 24 distinct bimodal logics for all logics we provide both ...

Predicate Change
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200326
Abstract:
Like belief revision, conceptual change has rational aspects. The paper discusses this for predicate change. We determine the meaning of predicates by a set of imaginable instances, i.e., conceptually consistent entities that fall under the predicate. Predicate change is then an alteration of which possible entities are instances of a concept. The recent exclusion of Pluto from the category of planets is an example of such a predicate change. In order to discuss predicate change, we define a monadic predicate logic with three different kinds of lawful belief: analytic laws, which hold for all possible instances; doxastic laws, which hold for the most plausible instances; and typicality laws, which hold for typical instances. We introduce predicate changing operations that alter the analytic laws of the language and show that the expressive power is not affected by the predicate change. One can translate the new laws into old laws and vice versa. Moreover, we discuss rational restrictions of predicate change. These limit its possible influence on doxastic and typicality laws. Based on the results, we argue that predicate change can be quite conservative and sometimes even hardly recognisable. Word Count:
Rank  Word  Count 
0  predicate  10 
Excerpts:
...rational aspects the paper discusses this for predicate change we determine the meaning of predicates ...
...conceptually consistent entities that fall under the predicate predicate change is then an alteration of ...
...consistent entities that fall under the predicate predicate change is then an alteration of which ...
...planets is an example of such a predicate change in order to discuss predicate change ...
...a predicate change in order to discuss predicate change we define a monadic predicate logic ...
...discuss predicate change we define a monadic predicate logic with three different kinds of lawful ...
...which hold for typical instances we introduce predicate changing operations that alter the analytic laws ...
...expressive power is not affected by the predicate change one can translate the new laws ...
...versa moreover we discuss rational restrictions of predicate change these limit its possible influence on ...
...based on the results we argue that predicate change can be quite conservative and sometimes ...

1  change  8 
Excerpts:
... like belief revision conceptual change has rational aspects the paper discusses this ...
...aspects the paper discusses this for predicate change we determine the meaning of predicates by ...
...entities that fall under the predicate predicate change is then an alteration of which possible ...
...is an example of such a predicate change in order to discuss predicate change we ...
...predicate change in order to discuss predicate change we define a monadic predicate logic with ...
...power is not affected by the predicate change one can translate the new laws into ...
...moreover we discuss rational restrictions of predicate change these limit its possible influence on doxastic ...
...on the results we argue that predicate change can be quite conservative and sometimes even ...

2  laws  7 
Excerpts:
...three different kinds of lawful belief analytic laws which hold for all possible instances doxastic ...
...which hold for all possible instances doxastic laws which hold for the most plausible instances ...
...for the most plausible instances and typicality laws which hold for typical instances we introduce ...
...predicate changing operations that alter the analytic laws of the language and show that the ...
...predicate change one can translate the new laws into old laws and vice versa moreover ...
...can translate the new laws into old laws and vice versa moreover we discuss rational ...
...its possible influence on doxastic and typicality laws based on the results we argue that ...

3  instances  5 
Excerpts:
...of predicates by a set of imaginable instances ie conceptually consistent entities that fall under ...
...an alteration of which possible entities are instances of a concept the recent exclusion of ...
...analytic laws which hold for all possible instances doxastic laws which hold for the most ...
...laws which hold for the most plausible instances and typicality laws which hold for typical ...
...and typicality laws which hold for typical instances we introduce predicate changing operations that alter ...

4  hold  3 
Excerpts:
...kinds of lawful belief analytic laws which hold for all possible instances doxastic laws which ...
...for all possible instances doxastic laws which hold for the most plausible instances and typicality ...
...most plausible instances and typicality laws which hold for typical instances we introduce predicate changing ...

5  possible  3 
Excerpts:
...change is then an alteration of which possible entities are instances of a concept the ...
...belief analytic laws which hold for all possible instances doxastic laws which hold for the ...
...restrictions of predicate change these limit its possible influence on doxastic and typicality laws based ...

6  analytic  2 
Excerpts:
...with three different kinds of lawful belief analytic laws which hold for all possible instances ...
...introduce predicate changing operations that alter the analytic laws of the language and show that ...

7  rational  2 
Excerpts:
... like belief revision conceptual change has rational aspects the paper discusses this for predicate ...
...laws and vice versa moreover we discuss rational restrictions of predicate change these limit its ...

8  belief  2 
Excerpts:
... like belief revision conceptual change has rational aspects the ...
...logic with three different kinds of lawful belief analytic laws which hold for all possible ...

9  typicality  2 
Excerpts:
...hold for the most plausible instances and typicality laws which hold for typical instances we ...
...limit its possible influence on doxastic and typicality laws based on the results we argue ...

Revising Probabilities and Full Beliefs
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200319
Abstract:
A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information that gives her sufficient reasons to do so. Such a proposition is (presently) undoubted, but not undoubtable (incorrigible). In the formal model it is assigned a probability 1 ˆ’ Î´, where Î´ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on (dichotomous) belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a (logically closed) belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change. Word Count:
Jeffrey Meets Kolmogorov
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200302
Abstract:
Jeffrey conditionalization is a rule for updating degrees of belief in light of uncertain evidence. It is usually assumed that the partitions involved in Jeffrey conditionalization are finite and only contain positivecredence elements. But there are interesting examples, involving continuous quantities, in which this is not the case. Q1 Can Jeffrey conditionalization be generalized to accommodate continuous cases? Meanwhile, several authors, such as Kenny Easwaran and Michael Rescorla, have been interested in Kolmogorov's theory of regular conditional distributions (rcds) as a possible framework for conditional probability which handles probabilityzero events. However the theory faces a major shortcoming: it seems messy and ad hoc. Q2 Is there some axiomatic theory which would justify and constrain the use of rcds, thus serving as a possible foundation for conditional probability? These two questions appear unrelated, but they are not, and this paper answers both. We show that when one appropriately generalizes Jeffrey conditionalization as in Q1, one obtains a framework which necessitates the use of rcds. It is then a short step to develop a general theory which addresses Q2, which we call the theory of extensions. The theory is a formal model of conditioning which recovers Bayesian conditionalization, Jeffrey conditionalization, and conditionalization via rcds as special cases. Word Count:
Rank  Word  Count 
0  conditionalization  7 
Excerpts:
... jeffrey conditionalization is a rule for updating degrees of ...
...assumed that the partitions involved in jeffrey conditionalization are finite and only contain positivecredence elements ...
...is not the case q1 can jeffrey conditionalization be generalized to accommodate continuous cases meanwhile ...
...show that when one appropriately generalizes jeffrey conditionalization as in q1 one obtains a framework ...
...formal model of conditioning which recovers bayesian conditionalization jeffrey conditionalization and conditionalization via rcds as ...
...of conditioning which recovers bayesian conditionalization jeffrey conditionalization and conditionalization via rcds as special cases ...
...which recovers bayesian conditionalization jeffrey conditionalization and conditionalization via rcds as special cases ...

1  theory  6 
Excerpts:
...michael rescorla have been interested in kolmogorovs theory of regular conditional distributions rcds as a ...
...probability which handles probabilityzero events however the theory faces a major shortcoming it seems messy ...
...ad hoc q2 is there some axiomatic theory which would justify and constrain the use ...
...a short step to develop a general theory which addresses q2 which we call the ...
...which addresses q2 which we call the theory of extensions the theory is a formal ...
...we call the theory of extensions the theory is a formal model of conditioning which ...

2  jeffrey  5 
Excerpts:
... jeffrey conditionalization is a rule for updating degrees ...
...usually assumed that the partitions involved in jeffrey conditionalization are finite and only contain positivecredence ...
...this is not the case q1 can jeffrey conditionalization be generalized to accommodate continuous cases ...
...we show that when one appropriately generalizes jeffrey conditionalization as in q1 one obtains a ...
...model of conditioning which recovers bayesian conditionalization jeffrey conditionalization and conditionalization via rcds as special ...

3  rcds  4 
Excerpts:
...in kolmogorovs theory of regular conditional distributions rcds as a possible framework for conditional probability ...
...would justify and constrain the use of rcds thus serving as a possible foundation for ...
...a framework which necessitates the use of rcds it is then a short step to ...
...bayesian conditionalization jeffrey conditionalization and conditionalization via rcds as special cases ...

4  conditional  3 
Excerpts:
...been interested in kolmogorovs theory of regular conditional distributions rcds as a possible framework for ...
...distributions rcds as a possible framework for conditional probability which handles probabilityzero events however the ...
...thus serving as a possible foundation for conditional probability these two questions appear unrelated but ...

5  continuous  2 
Excerpts:
...elements but there are interesting examples involving continuous quantities in which this is not the ...
...can jeffrey conditionalization be generalized to accommodate continuous cases meanwhile several authors such as kenny ...

6  use  2 
Excerpts:
...theory which would justify and constrain the use of rcds thus serving as a possible ...
...one obtains a framework which necessitates the use of rcds it is then a short ...

7  q2  2 
Excerpts:
...shortcoming it seems messy and ad hoc q2 is there some axiomatic theory which would ...
...to develop a general theory which addresses q2 which we call the theory of extensions ...

8  framework  2 
Excerpts:
...regular conditional distributions rcds as a possible framework for conditional probability which handles probabilityzero events ...
...conditionalization as in q1 one obtains a framework which necessitates the use of rcds it ...

9  possible  2 
Excerpts:
...of regular conditional distributions rcds as a possible framework for conditional probability which handles probabilityzero ...
...use of rcds thus serving as a possible foundation for conditional probability these two questions ...

Transfinite Metainferences
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200221
Abstract:
In Barrio et al. (Forthcoming) Barrio Pailos and Szmuc prove that there are systems of logic that agree with classical logic up to any finite metainferential level, and disagree with it thereafter. This article presents a generalized sense of metainference that extends into the transfinite, and proves analogous results to all transfinite orders. Word Count:
Rank  Word  Count 
0  transfinite  2 
Excerpts:
...sense of metainference that extends into the transfinite and proves analogous results to all transfinite ...
...transfinite and proves analogous results to all transfinite orders ...

1  barrio  2 
Excerpts:
... in barrio et al forthcoming barrio pailos and szmuc ...
... in barrio et al forthcoming barrio pailos and szmuc prove that there are ...

2  logic  2 
Excerpts:
...szmuc prove that there are systems of logic that agree with classical logic up to ...
...systems of logic that agree with classical logic up to any finite metainferential level and ...

3  thereafter  1 
Excerpts:
...finite metainferential level and disagree with it thereafter this article presents a generalized sense of ...

4  all  1 
Excerpts:
...the transfinite and proves analogous results to all transfinite orders ...

5  results  1 
Excerpts:
...extends into the transfinite and proves analogous results to all transfinite orders ...

6  analogous  1 
Excerpts:
...that extends into the transfinite and proves analogous results to all transfinite orders ...

7  proves  1 
Excerpts:
...metainference that extends into the transfinite and proves analogous results to all transfinite orders ...

8  into  1 
Excerpts:
...a generalized sense of metainference that extends into the transfinite and proves analogous results to ...

9  extends  1 
Excerpts:
...presents a generalized sense of metainference that extends into the transfinite and proves analogous results ...

Probability Modals and Infinite Domains
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200220
Abstract:
Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of probabilistic' semantics are often motivated by their ability to explain intuitions about inferences involving likely' and probably''intuitions that Angelika Kratzer's canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to undercut this motivation: they present a worldordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of worldordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard's semantics yields an adequate logic only if models are restricted to Noetherian preorders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. Word Count:
Rank  Word  Count 
0  semantics  10 
Excerpts:
...the mathematical theory of probability to the semantics of natural language probability talk these sorts ...
...language probability talk these sorts of probabilistic semantics are often motivated by their ability to ...
...likely and probablyintuitions that angelika kratzers canonical semantics fails to accommodate through a semantics based ...
...canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds ...
...undercut this motivation they present a worldordering semantics that yields essentially the same logic as ...
...yields essentially the same logic as probabilistic semantics in this paper i argue that the ...
...that the challenge remains defenders of worldordering semantics have yet to offer a plausible semantics ...
...semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood ...
...logic of comparative likelihood holliday amp icards semantics yields an adequate logic only if models ...
...of epistemic possibilities as a result probabilistic semantics remains the better explanation of the data ...

1  logic  3 
Excerpts:
...worldordering semantics that yields essentially the same logic as probabilistic semantics in this paper i ...
...offer a plausible semantics that captures the logic of comparative likelihood holliday amp icards semantics ...
...holliday amp icards semantics yields an adequate logic only if models are restricted to noetherian ...

2  probabilistic  3 
Excerpts:
...natural language probability talk these sorts of probabilistic semantics are often motivated by their ability ...
...that yields essentially the same logic as probabilistic semantics in this paper i argue that ...
...domains of epistemic possibilities as a result probabilistic semantics remains the better explanation of the ...

3  recent  2 
Excerpts:
... recent years have witnessed a proliferation of attempts ...
...and a qualitative ranking of propositions however recent work by wesley holliday and thomas icard ...

4  holliday  2 
Excerpts:
...of propositions however recent work by wesley holliday and thomas icard has been widely thought ...
...that captures the logic of comparative likelihood holliday amp icards semantics yields an adequate logic ...

5  worldordering  2 
Excerpts:
...to undercut this motivation they present a worldordering semantics that yields essentially the same logic ...
...argue that the challenge remains defenders of worldordering semantics have yet to offer a plausible ...

6  yields  2 
Excerpts:
...motivation they present a worldordering semantics that yields essentially the same logic as probabilistic semantics ...
...of comparative likelihood holliday amp icards semantics yields an adequate logic only if models are ...

7  remains  2 
Excerpts:
...this paper i argue that the challenge remains defenders of worldordering semantics have yet to ...
...epistemic possibilities as a result probabilistic semantics remains the better explanation of the data ...

8  noetherian  2 
Excerpts:
...logic only if models are restricted to noetherian preorders but i argue that the noetherian ...
...noetherian preorders but i argue that the noetherian restriction faces problems in cases involving infinitely ...

9  involving  2 
Excerpts:
...their ability to explain intuitions about inferences involving likely and probablyintuitions that angelika kratzers canonical ...
...the noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities as ...

A StateofAffairsSemantic Solution to the Problem of Extensionality in Free Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200220
Abstract:
If one takes seriously the idea that a scientific language must be extensional, and accepts Quine's notion of truthvaluerelated extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ˜extensionality', so that it would not be the truthvalue that had to be preserved under the substitution of coextensional expressions, but the state of affairs that the sentence described. The question is whether or not elementary sentences containing empty singular terms, such as ˜Vulcan rotates', are extensional in the substitutivity sense. Five conditions are specified under which extensionality in the substitutivity sense of such sentences can be secured. It is demonstrated that such sentences are stateofaffairsasextensionrelated extensional. This implies (in accordance with the basic idea of stateofaffairs semantics) that such sentences are also truthvaluerelated extensional in Quine's sense, but not truthvalueasextensionrelated extensional. Word Count:
Intuitionism and the Modal Logic of Vagueness
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200213
Abstract:
Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the socalled paradoxes of higherorder vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist's characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ˜it is clearly the case that'. S4M opens the way to an account of higherorder vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus (IPC) and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson's objections to intuitionistic treatments of vagueness. Word Count:
Author Correction: SupervaluationStyle Truth Without Supervaluations
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
Abstract:
The original version of the article unfortunately contained a mistake. In the Acknowledgments section of the original version of the article, the grant number of the Marie SklodowskaCurie Individual Fellowship supporting the author's work was misstated. Word Count:
Rank  Word  Count 
0  original  2 
Excerpts:
... the original version of the article unfortunately contained a ...
...mistake in the acknowledgments section of the original version of the article the grant number ...

1  version  2 
Excerpts:
... the original version of the article unfortunately contained a mistake ...
...in the acknowledgments section of the original version of the article the grant number of ...

2  article  2 
Excerpts:
... the original version of the article unfortunately contained a mistake in the acknowledgments ...
...section of the original version of the article the grant number of the marie sklodowskacurie ...

3  work  1 
Excerpts:
...marie sklodowskacurie individual fellowship supporting the authors work was misstated ...

4  authors  1 
Excerpts:
...the marie sklodowskacurie individual fellowship supporting the authors work was misstated ...

5  supporting  1 
Excerpts:
...number of the marie sklodowskacurie individual fellowship supporting the authors work was misstated ...

6  fellowship  1 
Excerpts:
...grant number of the marie sklodowskacurie individual fellowship supporting the authors work was misstated ...

7  individual  1 
Excerpts:
...the grant number of the marie sklodowskacurie individual fellowship supporting the authors work was misstated ...

8  sklodowskacurie  1 
Excerpts:
...article the grant number of the marie sklodowskacurie individual fellowship supporting the authors work was ...

9  number  1 
Excerpts:
...original version of the article the grant number of the marie sklodowskacurie individual fellowship supporting ...

A Hierarchy of Classical and Paraconsistent Logics
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
Abstract:
In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of stricttolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be nonidentical even if they share the same valid inferences. Word Count:
Rank  Word  Count 
0  logic  5 
Excerpts:
...a number of technical results concerning classical logic st and related systems our main contribution ...
...logics in general and therefore for classical logic in particular we will firstly generalize the ...
...entirely classical we will claim that a logic is to be identified with an infinite ...
...proposal allows not only to differentiate classical logic from st but also from other systems ...
...consequences for some topics in the philosophical logic literature among them for the debate around ...

1  classical  5 
Excerpts:
...present a number of technical results concerning classical logic st and related systems our main ...
...for logics in general and therefore for classical logic in particular we will firstly generalize ...
...logics in this hierarchy are progressively more classical although not entirely classical we will claim ...
...are progressively more classical although not entirely classical we will claim that a logic is ...
...present proposal allows not only to differentiate classical logic from st but also from other ...

2  will  5 
Excerpts:
... in this article we will present a number of technical results concerning ...
...therefore for classical logic in particular we will firstly generalize the st phenomenon thereby obtaining ...
...defined hierarchy of stricttolerant systems secondly we will prove that the logics in this hierarchy ...
...more classical although not entirely classical we will claim that a logic is to be ...
...employing a rivalry criterion for logics that will need to be modified in light of ...

3  logics  4 
Excerpts:
...in offering a novel identity criterion for logics in general and therefore for classical logic ...
...systems secondly we will prove that the logics in this hierarchy are progressively more classical ...
...carried out employing a rivalry criterion for logics that will need to be modified in ...
...the present investigation according to which two logics can be nonidentical even if they share ...

4  present  3 
Excerpts:
... in this article we will present a number of technical results concerning classical ...
...and so on as a result the present proposal allows not only to differentiate classical ...
...to be modified in light of the present investigation according to which two logics can ...

5  st  3 
Excerpts:
...number of technical results concerning classical logic st and related systems our main contribution consists ...
...in particular we will firstly generalize the st phenomenon thereby obtaining a recursively defined hierarchy ...
...not only to differentiate classical logic from st but also from other systems sharing with ...

6  systems  3 
Excerpts:
...results concerning classical logic st and related systems our main contribution consists in offering a ...
...obtaining a recursively defined hierarchy of stricttolerant systems secondly we will prove that the logics ...
...logic from st but also from other systems sharing with it their valid metainferences finally ...

7  valid  2 
Excerpts:
...from other systems sharing with it their valid metainferences finally we show how these results ...
...nonidentical even if they share the same valid inferences ...

8  metainferences  2 
Excerpts:
...holding between increasingly complex relata formulae inferences metainferences and so on as a result the ...
...other systems sharing with it their valid metainferences finally we show how these results have ...

9  inferences  2 
Excerpts:
...relations holding between increasingly complex relata formulae inferences metainferences and so on as a result ...
...even if they share the same valid inferences ...

The logic of ground
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
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:
Explicating Logical Independence
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
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:
On Hierarchical Propositions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
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:
Substitution contradiction, its resolution and the ChurchRosser Theorem in TIL
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
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  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 ...

3  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 ...

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

8  new  1 
Excerpts:
...in resolving the contradiction i provide a new amended definition of collisionless substitution which blocks ...

9  collisionless  1 
Excerpts:
...i provide a new amended definition of collisionless substitution which blocks the contradiction in a ...

Expectation Biases and Context Management with Negative Polar Questions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200201
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:
Infinitesimal Gunk
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200122
Abstract:
In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson's (1966) nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius (2008) and Russell (2008), which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors suggested. Unlike Arntzenius's proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell's proposal and does not retreat to mere finite additivity. Word Count:
Rank  Word  Count 
0  does  2 
Excerpts:
...these authors suggested unlike arntzeniuss proposal it does not introduce regions with no interior it ...
...richer measure theory than russells proposal and does not retreat to mere finite additivity ...

1  proposal  2 
Excerpts:
...alternative views these authors suggested unlike arntzeniuss proposal it does not introduce regions with no ...
...a much richer measure theory than russells proposal and does not retreat to mere finite ...

2  space  2 
Excerpts:
...an original view of the structure of space called infinitesimal gunk this view says that ...
...this view says that every region of space can be further divided and some regions ...

3  infinitesimal  2 
Excerpts:
...view of the structure of space called infinitesimal gunk this view says that every region ...
...be further divided and some regions have infinitesimal size where infinitesimals are understood in the ...

4  regions  2 
Excerpts:
...space can be further divided and some regions have infinitesimal size where infinitesimals are understood ...
...unlike arntzeniuss proposal it does not introduce regions with no interior it also has a ...

5  approach  1 
Excerpts:
...which have troubled a more familiar gunky approach moreover it has important advantages over the ...

6  moreover  1 
Excerpts:
...have troubled a more familiar gunky approach moreover it has important advantages over the alternative ...

7  important  1 
Excerpts:
...more familiar gunky approach moreover it has important advantages over the alternative views these authors ...

8  advantages  1 
Excerpts:
...familiar gunky approach moreover it has important advantages over the alternative views these authors suggested ...

9  over  1 
Excerpts:
...gunky approach moreover it has important advantages over the alternative views these authors suggested unlike ...

A Relevant Logic of Questions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200121
Abstract:
This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to RoutleyMeyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between RoutleyMeyer semantics and the semantics for InqR is also discussed. Word Count:
Rank  Word  Count 
0  semantics  5 
Excerpts:
...as the background logic of declaratives a semantics for inqr is developed and it is ...
...developed and it is shown that this semantics is in a precisely defined sense dual ...
...a precisely defined sense dual to routleymeyer semantics for r moreover inqr is axiomatized and ...
...philosophical interpretation of the duality between routleymeyer semantics and the semantics for inqr is also ...
...the duality between routleymeyer semantics and the semantics for inqr is also discussed ...

1  inqr  4 
Excerpts:
...the inquisitive extension of r denoted as inqr which is a relevant logic of questions ...
...background logic of declaratives a semantics for inqr is developed and it is shown that ...
...dual to routleymeyer semantics for r moreover inqr is axiomatized and completeness of the axiomatic ...
...between routleymeyer semantics and the semantics for inqr is also discussed ...

2  r  3 
Excerpts:
...this paper introduces the inquisitive extension of r denoted as inqr which is a relevant ...
...logic of questions based on the logic r as the background logic of declaratives a ...
...defined sense dual to routleymeyer semantics for r moreover inqr is axiomatized and completeness of ...

3  logic  3 
Excerpts:
...denoted as inqr which is a relevant logic of questions based on the logic r ...
...relevant logic of questions based on the logic r as the background logic of declaratives ...
...on the logic r as the background logic of declaratives a semantics for inqr is ...

4  routleymeyer  2 
Excerpts:
...in a precisely defined sense dual to routleymeyer semantics for r moreover inqr is axiomatized ...
...the philosophical interpretation of the duality between routleymeyer semantics and the semantics for inqr is ...

5  introduces  1 
Excerpts:
... this paper introduces the inquisitive extension of r denoted as ...

6  dual  1 
Excerpts:
...semantics is in a precisely defined sense dual to routleymeyer semantics for r moreover inqr ...

7  duality  1 
Excerpts:
...is established the philosophical interpretation of the duality between routleymeyer semantics and the semantics for ...

8  interpretation  1 
Excerpts:
...the axiomatic system is established the philosophical interpretation of the duality between routleymeyer semantics and ...

9  philosophical  1 
Excerpts:
...of the axiomatic system is established the philosophical interpretation of the duality between routleymeyer semantics ...

Logics of Synonymy
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200109
Abstract:
We investigate synonymy in the strong sense of content identity (and not just meaning similarity). This notion is central in the philosophy of language and in applications of logic. We motivate, uniformly axiomatize, and characterize several benchmark' notions of synonymy in the messy class of all possible notions of synonymy. This class is divided by two intuitive principles that are governed by a nogo result. We use the notion of a scenario to get a logic of synonymy (SF) which is the canonical representative of one division. In the other division, the socalled conceptivist logics, we find, e.g., the wellknown system of analytic containment (AC). We axiomatize four logics of synonymy extending AC, relate them semantically and prooftheoretically to SF, and characterize them in terms of weak/strong subject matter preservation and weak/strong logical equivalence. This yields ways out of the nogo result and novel arguments'independent of a particular semantic framework'for each notion of synonymy discussed (using, e.g., Hurford disjunctions or homotopy theory). This points to pluralism about meaning and a certain noncompositionality of truth in logic programs and neural networks. And it unveils an impossibility for synonymy: if it is to preserve subject matter, then either conjunction and disjunction lose an essential property or a very weak absorption law is violated. Word Count:
Rank  Word  Count 
0  synonymy  7 
Excerpts:
... we investigate synonymy in the strong sense of content identity ...
...axiomatize and characterize several benchmark notions of synonymy in the messy class of all possible ...
...messy class of all possible notions of synonymy this class is divided by two intuitive ...
...a scenario to get a logic of synonymy sf which is the canonical representative of ...
...containment ac we axiomatize four logics of synonymy extending ac relate them semantically and prooftheoretically ...
...a particular semantic frameworkfor each notion of synonymy discussed using eg hurford disjunctions or homotopy ...
...networks and it unveils an impossibility for synonymy if it is to preserve subject matter ...

1  logic  3 
Excerpts:
...philosophy of language and in applications of logic we motivate uniformly axiomatize and characterize several ...
...notion of a scenario to get a logic of synonymy sf which is the canonical ...
...and a certain noncompositionality of truth in logic programs and neural networks and it unveils ...

2  notion  3 
Excerpts:
...identity and not just meaning similarity this notion is central in the philosophy of language ...
...by a nogo result we use the notion of a scenario to get a logic ...
...argumentsindependent of a particular semantic frameworkfor each notion of synonymy discussed using eg hurford disjunctions ...

3  weakstrong  2 
Excerpts:
...sf and characterize them in terms of weakstrong subject matter preservation and weakstrong logical equivalence ...
...terms of weakstrong subject matter preservation and weakstrong logical equivalence this yields ways out of ...

4  eg  2 
Excerpts:
...division the socalled conceptivist logics we find eg the wellknown system of analytic containment ac ...
...frameworkfor each notion of synonymy discussed using eg hurford disjunctions or homotopy theory this points ...

5  characterize  2 
Excerpts:
...of logic we motivate uniformly axiomatize and characterize several benchmark notions of synonymy in the ...
...them semantically and prooftheoretically to sf and characterize them in terms of weakstrong subject matter ...

6  axiomatize  2 
Excerpts:
...in applications of logic we motivate uniformly axiomatize and characterize several benchmark notions of synonymy ...
...wellknown system of analytic containment ac we axiomatize four logics of synonymy extending ac relate ...

7  sf  2 
Excerpts:
...scenario to get a logic of synonymy sf which is the canonical representative of one ...
...ac relate them semantically and prooftheoretically to sf and characterize them in terms of weakstrong ...

8  division  2 
Excerpts:
...which is the canonical representative of one division in the other division the socalled conceptivist ...
...representative of one division in the other division the socalled conceptivist logics we find eg ...

9  logics  2 
Excerpts:
...in the other division the socalled conceptivist logics we find eg the wellknown system of ...
...of analytic containment ac we axiomatize four logics of synonymy extending ac relate them semantically ...

Truthmaker Semantics for Relevant Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200107
Abstract:
I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. Word Count:
Rank  Word  Count 
0  semantics  4 
Excerpts:
... i develop and defend a truthmaker semantics for the relevant logic r the approach ...
...as to build a technically adequate relevant semantics the central philosophical idea is that truths ...
...developing the idea formally results in a semantics on which truthmakers are relevant to what ...
...contraposition and excluded middle within a truthmaker semantics ...

1  relevant  4 
Excerpts:
...and defend a truthmaker semantics for the relevant logic r the approach begins with a ...
...so as to build a technically adequate relevant semantics the central philosophical idea is that ...
...in a semantics on which truthmakers are relevant to what they make true a very ...
...notion of conditionality is added giving us relevant implication i then investigate ways to add ...

2  idea  3 
Excerpts:
...the approach begins with a simple philosophical idea and develops it in various directions so ...
...technically adequate relevant semantics the central philosophical idea is that truths are true in virtue ...
...in virtue of specific states developing the idea formally results in a semantics on which ...

3  truthmaker  2 
Excerpts:
... i develop and defend a truthmaker semantics for the relevant logic r the ...
...justify contraposition and excluded middle within a truthmaker semantics ...

4  true  2 
Excerpts:
...central philosophical idea is that truths are true in virtue of specific states developing the ...
...truthmakers are relevant to what they make true a very natural notion of conditionality is ...

5  philosophical  2 
Excerpts:
...r the approach begins with a simple philosophical idea and develops it in various directions ...
...a technically adequate relevant semantics the central philosophical idea is that truths are true in ...

6  develop  1 
Excerpts:
... i develop and defend a truthmaker semantics for the ...

7  ways  1 
Excerpts:
...giving us relevant implication i then investigate ways to add conjunction disjunction and negation and ...

8  natural  1 
Excerpts:
...to what they make true a very natural notion of conditionality is added giving us ...

9  notion  1 
Excerpts:
...what they make true a very natural notion of conditionality is added giving us relevant ...

Relative Necessity and Propositional Quantification
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191228
Abstract:
Following Smiley's (The Journal of Symbolic Logic, 28, 113“134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33“42 1981) and others have highlighted various flaws with Smiley's now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1“26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech's account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown modeltheoretically to meet several desiderata of an account of relative necessity. Word Count:
