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 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 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, 215231, 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 ...

A Hierarchy of Classical and Paraconsistent Logics
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190408
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  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 ...

2  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 ...

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  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 ...

5  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 ...

6  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 ...

7  criterion  2 
Excerpts:
...contribution consists in offering a novel identity criterion for logics in general and therefore for ...
...is usually carried out employing a rivalry criterion for logics that will need to be ...

8  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 ...

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 ...

Correction to: HYPE: A System of Hyperintensional Logic (with an Application to Semantic Paradoxes)
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
The original version of the article unfortunately contained a mistake. The author missed to mention the support by a EUfunded research network that he is involved in. See below. This work was supported by the MarieSklodowskaCurie Innovative Training Network DIAPHORA. Word Count:
Rank  Word  Count 
0  network  2 
Excerpts:
...mention the support by a eufunded research network that he is involved in see below ...
...was supported by the mariesklodowskacurie innovative training network diaphora ...

1  below  1 
Excerpts:
...network that he is involved in see below this work was supported by the mariesklodowskacurie ...

2  see  1 
Excerpts:
...research network that he is involved in see below this work was supported by the ...

3  involved  1 
Excerpts:
...a eufunded research network that he is involved in see below this work was supported ...

4  work  1 
Excerpts:
...he is involved in see below this work was supported by the mariesklodowskacurie innovative training ...

5  supported  1 
Excerpts:
...involved in see below this work was supported by the mariesklodowskacurie innovative training network diaphora ...

6  diaphora  1 
Excerpts:
...supported by the mariesklodowskacurie innovative training network diaphora ...

7  training  1 
Excerpts:
...work was supported by the mariesklodowskacurie innovative training network diaphora ...

8  innovative  1 
Excerpts:
...this work was supported by the mariesklodowskacurie innovative training network diaphora ...

9  mariesklodowskacurie  1 
Excerpts:
...below this work was supported by the mariesklodowskacurie innovative training network diaphora ...

Representation of Functions and Total Antisymmetric Relations in Monadic Third Order Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation of cardinality in this theory (a result already shown in a somewhat different way by Henrard in unpublished work, but our approach differs from his in providing representations of bijections between sets in a stronger sense). The relation of our work to similar work by Henrard (to whom we are indebted) and Allen Hazen (who arrived at related results independently) is discussed. This work can be understood as part of a program of assessing the capabilities of (relatively) weak logical frameworks: our results are applicable for example, to the framework in David Lewis's Parts of Classes. Word Count:
Rank  Word  Count 
0  relations  5 
Excerpts:
... we analyze the representation of binary relations in general and in particular of functions ...
...particular of functions and of total antisymmetric relations in monadic third order logic that is ...
...representation of functions or of total antisymmetric relations in this theory we present partial representations ...
...representations of functions and of total antisymmetric relations which work for large classes of these ...
...which work for large classes of these relations and show that there is an adequate ...

1  work  5 
Excerpts:
...functions and of total antisymmetric relations which work for large classes of these relations and ...
...somewhat different way by henrard in unpublished work but our approach differs from his in ...
...a stronger sense the relation of our work to similar work by henrard to whom ...
...the relation of our work to similar work by henrard to whom we are indebted ...
...at related results independently is discussed this work can be understood as part of a ...

2  total  3 
Excerpts:
...and in particular of functions and of total antisymmetric relations in monadic third order logic ...
...no general representation of functions or of total antisymmetric relations in this theory we present ...
...present partial representations of functions and of total antisymmetric relations which work for large classes ...

3  antisymmetric  3 
Excerpts:
...in particular of functions and of total antisymmetric relations in monadic third order logic that ...
...general representation of functions or of total antisymmetric relations in this theory we present partial ...
...partial representations of functions and of total antisymmetric relations which work for large classes of ...

4  theory  3 
Excerpts:
...order logic that is the simple typed theory of sets with three types we show ...
...or of total antisymmetric relations in this theory we present partial representations of functions and ...
...an adequate representation of cardinality in this theory a result already shown in a somewhat ...

5  functions  3 
Excerpts:
...relations in general and in particular of functions and of total antisymmetric relations in monadic ...
...that there is no general representation of functions or of total antisymmetric relations in this ...
...this theory we present partial representations of functions and of total antisymmetric relations which work ...

6  representation  3 
Excerpts:
... we analyze the representation of binary relations in general and in ...
...we show that there is no general representation of functions or of total antisymmetric relations ...
...and show that there is an adequate representation of cardinality in this theory a result ...

7  sets  2 
Excerpts:
...that is the simple typed theory of sets with three types we show that there ...
...his in providing representations of bijections between sets in a stronger sense the relation of ...

8  show  2 
Excerpts:
...theory of sets with three types we show that there is no general representation of ...
...for large classes of these relations and show that there is an adequate representation of ...

9  representations  2 
Excerpts:
...relations in this theory we present partial representations of functions and of total antisymmetric relations ...
...our approach differs from his in providing representations of bijections between sets in a stronger ...

A Topological Approach to Full Belief
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
Stalnaker (Philosophical Studies, 128(1), 169199 2006) introduced a combined epistemicdoxastic logic that can formally express a strong concept of belief, a concept of belief as subjective certainty'. In this paper, we provide a topological semantics for belief, in particular, for Stalnaker's notion of belief defined as epistemic possibility of knowledge', in terms of the closure of the interior operator on extremally disconnected spaces. This semantics extends the standard topological interpretation of knowledge (as the interior operator) with a new topological semantics for belief. We prove that the belief logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. We also study (static) belief revision as well as belief dynamics by providing a topological semantics for conditional belief and belief update modalities, respectively. Our setting based on extremally disconnected spaces, however, encounters problems when extended with dynamic updates. We then propose a solution consisting in interpreting belief in a similar way based on hereditarily extremally disconnected spaces, and axiomatize the belief logic of hereditarily extremally disconnected spaces. Finally, we provide a complete axiomatization of the logic of conditional belief and knowledge, as well as a complete axiomatization of the corresponding dynamic logic. Word Count:
Bimodal Logics with Contingency and Accident
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its modeltheoretical properties such as expressivity and frame definability. We axiomatize this logic over various classes of frames, whose completeness proofs are shown with the help of a crucial schema. The interactions between contingency and accident can sharpen our understanding of both notions. Then we extend the logic to a dynamic case: public announcements. By finding the required reduction axioms, we obtain a complete axiomatization, which gives us a good application to Moore sentences. Word Count:
Rank  Word  Count 
0  logic  4 
Excerpts:
...two important notions in philosophy and philosophical logic their meanings are so close that they ...
...we propose a language of a bimodal logic with these two concepts investigate its modeltheoretical ...
...expressivity and frame definability we axiomatize this logic over various classes of frames whose completeness ...
...of both notions then we extend the logic to a dynamic case public announcements by ...

1  contingency  2 
Excerpts:
... contingency and accident are two important notions in ...
...of a crucial schema the interactions between contingency and accident can sharpen our understanding of ...

2  research  2 
Excerpts:
...sometimes in both daily life and academic research this indicates that it is necessary to ...
...framework however there has been no logical research on them together in this paper we ...

3  accident  2 
Excerpts:
... contingency and accident are two important notions in philosophy and ...
...crucial schema the interactions between contingency and accident can sharpen our understanding of both notions ...

4  both  2 
Excerpts:
...that they are mixed up sometimes in both daily life and academic research this indicates ...
...and accident can sharpen our understanding of both notions then we extend the logic to ...

5  them  2 
Excerpts:
...indicates that it is necessary to study them in a unified framework however there has ...
...there has been no logical research on them together in this paper we propose a ...

6  notions  2 
Excerpts:
... contingency and accident are two important notions in philosophy and philosophical logic their meanings ...
...accident can sharpen our understanding of both notions then we extend the logic to a ...

7  crucial  1 
Excerpts:
...are shown with the help of a crucial schema the interactions between contingency and accident ...

8  schema  1 
Excerpts:
...shown with the help of a crucial schema the interactions between contingency and accident can ...

9  interactions  1 
Excerpts:
...the help of a crucial schema the interactions between contingency and accident can sharpen our ...

Disentangling Structural Connectives or Life Without Display Property
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
The work is concerned with the so called display property of display logic. The motivation behind it is discussed and challenged. It is shown using one display calculus for intuitionistic logic as an example that the display property can be abandoned without losing subformula, cut elimination and completeness properties in such a way that results in additional expressive power of the system. This is done by disentangling structural connectives so that they are no longer contextsensitive. A recipe for characterizing structural extensions of display calculi is provided. Word Count:
Rank  Word  Count 
0  display  5 
Excerpts:
...work is concerned with the so called display property of display logic the motivation behind ...
...with the so called display property of display logic the motivation behind it is discussed ...
...and challenged it is shown using one display calculus for intuitionistic logic as an example ...
...intuitionistic logic as an example that the display property can be abandoned without losing subformula ...
...a recipe for characterizing structural extensions of display calculi is provided ...

1  property  2 
Excerpts:
...is concerned with the so called display property of display logic the motivation behind it ...
...logic as an example that the display property can be abandoned without losing subformula cut ...

2  structural  2 
Excerpts:
...the system this is done by disentangling structural connectives so that they are no longer ...
...no longer contextsensitive a recipe for characterizing structural extensions of display calculi is provided ...

3  logic  2 
Excerpts:
...the so called display property of display logic the motivation behind it is discussed and ...
...shown using one display calculus for intuitionistic logic as an example that the display property ...

4  system  1 
Excerpts:
...results in additional expressive power of the system this is done by disentangling structural connectives ...

5  done  1 
Excerpts:
...expressive power of the system this is done by disentangling structural connectives so that they ...

6  disentangling  1 
Excerpts:
...of the system this is done by disentangling structural connectives so that they are no ...

7  power  1 
Excerpts:
...a way that results in additional expressive power of the system this is done by ...

8  expressive  1 
Excerpts:
...such a way that results in additional expressive power of the system this is done ...

9  way  1 
Excerpts:
...elimination and completeness properties in such a way that results in additional expressive power of ...

Bilateralism, Trilateralism, Multilateralism and PolySequents
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
The paper introduces the formula structure of polysequents, allowing the expression of polypositions: positions with any number of stances, of which bilateralism and trilateralism are special cases. The paper also puts forward the view that scoherence (strong coherence) of such polypositions can be defined inferentially, without appealing to their validity under interpretations of the object language. Word Count:
Rank  Word  Count 
0  polypositions  2 
Excerpts:
...structure of polysequents allowing the expression of polypositions positions with any number of stances of ...
...view that scoherence strong coherence of such polypositions can be defined inferentially without appealing to ...

1  inferentially  1 
Excerpts:
...coherence of such polypositions can be defined inferentially without appealing to their validity under interpretations ...

2  without  1 
Excerpts:
...of such polypositions can be defined inferentially without appealing to their validity under interpretations of ...

3  defined  1 
Excerpts:
...strong coherence of such polypositions can be defined inferentially without appealing to their validity under ...

4  coherence  1 
Excerpts:
...puts forward the view that scoherence strong coherence of such polypositions can be defined inferentially ...

5  scoherence  1 
Excerpts:
...paper also puts forward the view that scoherence strong coherence of such polypositions can be ...

6  strong  1 
Excerpts:
...also puts forward the view that scoherence strong coherence of such polypositions can be defined ...

7  appealing  1 
Excerpts:
...such polypositions can be defined inferentially without appealing to their validity under interpretations of the ...

8  their  1 
Excerpts:
...can be defined inferentially without appealing to their validity under interpretations of the object language ...

9  object  1 
Excerpts:
...to their validity under interpretations of the object language ...

A ThreeValued Fregean Quantification Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
Kripke's Fregean quantification logic FQ fails to formalize the usual firstorder logic with identity due to the interpretation of the conditional operator. Motivated by Kripke's syntax and semantics, the threevalued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz's threevalued logics. The logic FQ3 is decidable. A sound and complete Hilbertstyle axiomatic system for the logic FQ3 is presented. Word Count:
Rank  Word  Count 
0  logic  6 
Excerpts:
... kripkes fregean quantification logic fq fails to formalize the usual firstorder ...
...fq fails to formalize the usual firstorder logic with identity due to the interpretation of ...
...syntax and semantics the threevalued fregean quantification logic fq3 is proposed this three valued logic ...
...logic fq3 is proposed this three valued logic differs from kleene and Łukasiewiczs threevalued logics ...
...from kleene and Łukasiewiczs threevalued logics the logic fq3 is decidable a sound and complete ...
...and complete hilbertstyle axiomatic system for the logic fq3 is presented ...

1  fq3  3 
Excerpts:
...and semantics the threevalued fregean quantification logic fq3 is proposed this three valued logic differs ...
...kleene and Łukasiewiczs threevalued logics the logic fq3 is decidable a sound and complete hilbertstyle ...
...complete hilbertstyle axiomatic system for the logic fq3 is presented ...

2  kripkes  2 
Excerpts:
... kripkes fregean quantification logic fq fails to formalize ...
...interpretation of the conditional operator motivated by kripkes syntax and semantics the threevalued fregean quantification ...

3  threevalued  2 
Excerpts:
...motivated by kripkes syntax and semantics the threevalued fregean quantification logic fq3 is proposed this ...
...valued logic differs from kleene and Łukasiewiczs threevalued logics the logic fq3 is decidable a ...

4  quantification  2 
Excerpts:
... kripkes fregean quantification logic fq fails to formalize the usual ...
...kripkes syntax and semantics the threevalued fregean quantification logic fq3 is proposed this three valued ...

5  fregean  2 
Excerpts:
... kripkes fregean quantification logic fq fails to formalize the ...
...by kripkes syntax and semantics the threevalued fregean quantification logic fq3 is proposed this three ...

6  Łukasiewiczs  1 
Excerpts:
...three valued logic differs from kleene and Łukasiewiczs threevalued logics the logic fq3 is decidable ...

7  kleene  1 
Excerpts:
...proposed this three valued logic differs from kleene and Łukasiewiczs threevalued logics the logic fq3 ...

8  valued  1 
Excerpts:
...quantification logic fq3 is proposed this three valued logic differs from kleene and Łukasiewiczs threevalued ...

9  logics  1 
Excerpts:
...logic differs from kleene and Łukasiewiczs threevalued logics the logic fq3 is decidable a sound ...

HYPE: A System of Hyperintensional Logic (with an Application to Semantic Paradoxes)
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190401
Abstract:
This article introduces, studies, and applies a new system of logic which is called HYPE'. In HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth value gluts (overdeterminedness). Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the predicate logic of the system. The propositional logic of HYPE is shown to contain firstdegree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE's logical connectives. Furthermore, HYPE's firstorder logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive EulerVennlike diagrams, and its logical structure matches structures wellknown from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, manyvalued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of typefree truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending nonclassical fixedpoint interpretations of truth by a conditional as wellbehaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to followup work. Word Count:
Author Correction: SupervaluationStyle Truth Without Supervaluations
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190313
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  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 ...

2  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 ...

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

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

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

Models for Hylomorphism
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190311
Abstract:
In a series of papers (Fine et al., 1982; Fine, Noûs28(2), 137158; 1994, Midwest Studies in Philosophy, 23, 6174, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in (Midwest Studies in Philosophy, 23, 6174, 1999). In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the secondorder quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine's principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine's various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki's (2008) main objection to Fine's theory. In the appendix we present proofs of the inexpressibility results of Section 6. Word Count:
Substitution Structures
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190226
Abstract:
Word Count:
Algebraic Analysis of Demodalised Analytic Implication
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190213
Abstract:
The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn (and independently investigated by R.D. Epstein) as a variation on a timehonoured logical system by C.I. Lewis' student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is analytically contained' in its antecedent. DAI has been investigated both prooftheoretically and modeltheoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of involutive bisemilattices, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic (PWK). This fact sheds further light on the relationship between containment logics and logics of nonsense. Word Count:
Rank  Word  Count 
0  dai  5 
Excerpts:
... the logic dai of demodalised analytic implication has been introduced ...
...consequent is analytically contained in its antecedent dai has been investigated both prooftheoretically and modeltheoretically ...
...no study so far has focussed on dai from the viewpoint of abstract algebraic logic ...
...we provide several different algebraic semantics for dai showing their equivalence with the known semantics ...
...dunn and epstein we also show that dai is algebraisable and we identify its equivalent ...

1  logic  4 
Excerpts:
... the logic dai of demodalised analytic implication has been ...
...wt parry the main tenet underlying this logic is that no implication can be valid ...
...dai from the viewpoint of abstract algebraic logic we provide several different algebraic semantics for ...
...the algebraic counterpart of paraconsistent weak kleene logic pwk this fact sheds further light on ...

2  semantics  3 
Excerpts:
...algebraic logic we provide several different algebraic semantics for dai showing their equivalence with the ...
...dai showing their equivalence with the known semantics by dunn and epstein we also show ...
...algebraisable and we identify its equivalent quasivariety semantics this class turns out to be a ...

3  algebraic  3 
Excerpts:
...on dai from the viewpoint of abstract algebraic logic we provide several different algebraic semantics ...
...abstract algebraic logic we provide several different algebraic semantics for dai showing their equivalence with ...
...bisemilattices a subquasivariety of which forms the algebraic counterpart of paraconsistent weak kleene logic pwk ...

4  investigated  2 
Excerpts:
...been introduced by jm dunn and independently investigated by rd epstein as a variation on ...
...contained in its antecedent dai has been investigated both prooftheoretically and modeltheoretically but no study ...

5  epstein  2 
Excerpts:
...jm dunn and independently investigated by rd epstein as a variation on a timehonoured logical ...
...with the known semantics by dunn and epstein we also show that dai is algebraisable ...

6  dunn  2 
Excerpts:
...analytic implication has been introduced by jm dunn and independently investigated by rd epstein as ...
...their equivalence with the known semantics by dunn and epstein we also show that dai ...

7  logics  2 
Excerpts:
...further light on the relationship between containment logics and logics of nonsense ...
...on the relationship between containment logics and logics of nonsense ...

8  implication  2 
Excerpts:
... the logic dai of demodalised analytic implication has been introduced by jm dunn and ...
...tenet underlying this logic is that no implication can be valid unless its consequent is ...

9  been  2 
Excerpts:
...logic dai of demodalised analytic implication has been introduced by jm dunn and independently investigated ...
...analytically contained in its antecedent dai has been investigated both prooftheoretically and modeltheoretically but no ...

Disappearing Diamonds: FitchLike Results in Bimodal Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190209
Abstract:
Augment the propositional language with two modal operators: and . Define
\(\blacklozenge \)
to be the dual of , i.e.
\(\blacklozenge \equiv \neg \blacksquare \neg \)
. Whenever (X) is of the form φ ψ, let (X
\(^{\blacklozenge } \)
) be
\(\varphi \rightarrow \blacklozenge \psi \)
. (X
\(^{\blacklozenge } \)
) can be thought of as the modally qualified counterpart of (X)'for instance, under the metaphysical interpretation of
\(\blacklozenge \)
, where (X) says φ implies ψ, (X
\(^{\blacklozenge } \)
) says φ implies possiblyψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (X
\(^{\blacklozenge } \)
) to imply (X)'so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy. Word Count:
Simplified Tableaux for STIT Imagination Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190207
Abstract:
We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing (Journal of Philosophical Logic, 47(2), 259279, 2018). Word Count:
