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:
A Paraconsistent Conditional Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191220
Abstract:
We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas' conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system \(\mathcal {C}\) which is an extension of the BelnapDunn fourvalued logic with a conditional operator. Some acceptive extensions of \(\mathcal {C}\) are shown to be sound and complete. We also show the finite acceptive model property and decidability of these logics. Word Count:
Rank  Word  Count 
0  logic  3 
Excerpts:
... we develop a paraconsistent logic by introducing new models for conditionals with ...
...truth conditions of conditionals the paraconsistent conditional logic is axiomatized by a sequent system mathcal ...
...is an extension of the belnapdunn fourvalued logic with a conditional operator some acceptive extensions ...

1  acceptive  3 
Excerpts:
...by introducing new models for conditionals with acceptive and rejective selection functions which are variants ...
...fourvalued logic with a conditional operator some acceptive extensions of mathcal c are shown to ...
...and complete we also show the finite acceptive model property and decidability of these logics ...

2  conditional  3 
Excerpts:
...selection functions which are variants of chellas conditional models the acceptance and rejection conditions are ...
...for truth conditions of conditionals the paraconsistent conditional logic is axiomatized by a sequent system ...
...of the belnapdunn fourvalued logic with a conditional operator some acceptive extensions of mathcal c ...

3  mathcal  2 
Excerpts:
...logic is axiomatized by a sequent system mathcal c which is an extension of the ...
...a conditional operator some acceptive extensions of mathcal c are shown to be sound and ...

4  models  2 
Excerpts:
...develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection ...
...functions which are variants of chellas conditional models the acceptance and rejection conditions are substituted ...

5  conditionals  2 
Excerpts:
...paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which ...
...conditions are substituted for truth conditions of conditionals the paraconsistent conditional logic is axiomatized by ...

6  paraconsistent  2 
Excerpts:
... we develop a paraconsistent logic by introducing new models for conditionals ...
...substituted for truth conditions of conditionals the paraconsistent conditional logic is axiomatized by a sequent ...

7  c  2 
Excerpts:
...is axiomatized by a sequent system mathcal c which is an extension of the belnapdunn ...
...conditional operator some acceptive extensions of mathcal c are shown to be sound and complete ...

8  conditions  2 
Excerpts:
...chellas conditional models the acceptance and rejection conditions are substituted for truth conditions of conditionals ...
...and rejection conditions are substituted for truth conditions of conditionals the paraconsistent conditional logic is ...

9  extensions  1 
Excerpts:
...logic with a conditional operator some acceptive extensions of mathcal c are shown to be ...

The Fundamental Problem of Logical Omniscience
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191220
Abstract:
We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spinoff from a general theory of thick content, whereby the content of a sentence has two components: (i) an intension, taking care of truth conditions; and (ii) a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: (1) the topicsensitivity of content; (2) the fragmentation of knowledge states; (3) the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. Word Count:
Rank  Word  Count 
0  knowledge  5 
Excerpts:
...version as concerning arbitrary agents and the knowledge attitude per se our logic of knowledge ...
...knowledge attitude per se our logic of knowledge is a spinoff from a general theory ...
...validities and invalidities for the logic of knowledge per se for arbitrary agents and isolate ...
...topicsensitivity of content 2 the fragmentation of knowledge states 3 the defeasibility of knowledge acquisition ...
...of knowledge states 3 the defeasibility of knowledge acquisition we then present a novel dynamic ...

1  content  3 
Excerpts:
...spinoff from a general theory of thick content whereby the content of a sentence has ...
...general theory of thick content whereby the content of a sentence has two components i ...
...factors for them 1 the topicsensitivity of content 2 the fragmentation of knowledge states 3 ...

2  logic  3 
Excerpts:
...and the knowledge attitude per se our logic of knowledge is a spinoff from a ...
...plausible logical validities and invalidities for the logic of knowledge per se for arbitrary agents ...
...we then present a novel dynamic epistemic logic that yields precisely the desired validities and ...

3  arbitrary  2 
Excerpts:
...to be its fundamental version as concerning arbitrary agents and the knowledge attitude per se ...
...the logic of knowledge per se for arbitrary agents and isolate three explanatory factors for ...

4  care  2 
Excerpts:
...has two components i an intension taking care of truth conditions and ii a topic ...
...truth conditions and ii a topic taking care of subject matter we present a list ...

5  se  2 
Excerpts:
...arbitrary agents and the knowledge attitude per se our logic of knowledge is a spinoff ...
...invalidities for the logic of knowledge per se for arbitrary agents and isolate three explanatory ...

6  per  2 
Excerpts:
...concerning arbitrary agents and the knowledge attitude per se our logic of knowledge is a ...
...and invalidities for the logic of knowledge per se for arbitrary agents and isolate three ...

7  agents  2 
Excerpts:
...be its fundamental version as concerning arbitrary agents and the knowledge attitude per se our ...
...logic of knowledge per se for arbitrary agents and isolate three explanatory factors for them ...

8  invalidities  2 
Excerpts:
...a list of plausible logical validities and invalidities for the logic of knowledge per se ...
...that yields precisely the desired validities and invalidities for which we provide expressivity and completeness ...

9  logical  2 
Excerpts:
...propose a solution to the problem of logical omniscience in what we take to be ...
...matter we present a list of plausible logical validities and invalidities for the logic of ...

Intuitionistic Conditional Logics
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191218
Abstract:
Building on recent work by Yale Weiss, we study conditional logics in the intuitionistic setting. We consider a number of semantic conditions which give rise, among others, to intuitionistic counterparts of Lewis's logic VC and Stalnaker's C2. We show how to obtain a sound and complete axiomatization of each logic arising from a combination of these conditions. On the way, we remark how, in the intuitionistic setting, certain classically equivalent principles of conditional logic come apart, and how certain logical connections between different principles no longer hold. Word Count:
Rank  Word  Count 
0  intuitionistic  3 
Excerpts:
...weiss we study conditional logics in the intuitionistic setting we consider a number of semantic ...
...conditions which give rise among others to intuitionistic counterparts of lewiss logic vc and stalnakers ...
...the way we remark how in the intuitionistic setting certain classically equivalent principles of conditional ...

1  logic  3 
Excerpts:
...among others to intuitionistic counterparts of lewiss logic vc and stalnakers c2 we show how ...
...a sound and complete axiomatization of each logic arising from a combination of these conditions ...
...setting certain classically equivalent principles of conditional logic come apart and how certain logical connections ...

2  certain  2 
Excerpts:
...we remark how in the intuitionistic setting certain classically equivalent principles of conditional logic come ...
...of conditional logic come apart and how certain logical connections between different principles no longer ...

3  conditional  2 
Excerpts:
...recent work by yale weiss we study conditional logics in the intuitionistic setting we consider ...
...intuitionistic setting certain classically equivalent principles of conditional logic come apart and how certain logical ...

4  setting  2 
Excerpts:
...we study conditional logics in the intuitionistic setting we consider a number of semantic conditions ...
...way we remark how in the intuitionistic setting certain classically equivalent principles of conditional logic ...

5  principles  2 
Excerpts:
...in the intuitionistic setting certain classically equivalent principles of conditional logic come apart and how ...
...and how certain logical connections between different principles no longer hold ...

6  conditions  2 
Excerpts:
...setting we consider a number of semantic conditions which give rise among others to intuitionistic ...
...logic arising from a combination of these conditions on the way we remark how in ...

7  building  1 
Excerpts:
... building on recent work by yale weiss we ...

8  axiomatization  1 
Excerpts:
...how to obtain a sound and complete axiomatization of each logic arising from a combination ...

9  each  1 
Excerpts:
...obtain a sound and complete axiomatization of each logic arising from a combination of these ...

Disappearing Diamonds: FitchLike Results in Bimodal Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191201
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 Ï† †’ Ïˆ, 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 Ï† implies Ïˆ, (X\(^{\blacklozenge } \) ) says Ï† implies possiblyÏˆ. 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:
Algebraic Analysis of Demodalised Analytic Implication
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191201
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  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 ...

5  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 ...

6  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 ...

7  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 ...

8  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 ...

9  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 ...

Substitution Structures
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191201
Abstract:
Word Count:
Simplified Tableaux for STIT Imagination Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191201
Abstract:
We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing (Journal of Philosophical Logic, 47(2), 259“279, 2018). Word Count:
