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Proof-Relevant Logical Relations for Name Generation
[article]

2017
*
arXiv
*
pre-print

This paper presents a direct-style model of a ν-calculus-like language with recursion using the novel framework of

arXiv:1708.05193v1
fatcat:7awf2fmvqbbbllgiblm74amf3m
*proof*-*relevant**logical**relations*, in which*logical**relations*also contain objects (or ... Pitts and Stark's ν-calculus is a paradigmatic total language*for*studying the problem of contextual equivalence in higher-order languages with*name**generation*. ... We also show that the transition to*proof**relevance*makes the induced*logical**relation*transitive, which is*generally*not the case*for*ordinary Kripke*logical**relations*. S .u → w. ...##
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Proof-Relevant Logical Relations for Name Generation
[chapter]

2013
*
Lecture Notes in Computer Science
*

This paper presents a direct-style model of a ν-calculus-like language with recursion using the novel framework of

doi:10.1007/978-3-642-38946-7_6
fatcat:qxyfqkonajhilg4zc3pybwsehm
*proof*-*relevant**logical**relations*, in which*logical**relations*also contain objects (or ... Pitts and Stark's ν-calculus is a paradigmatic total language*for*studying the problem of contextual equivalence in higher-order languages with*name**generation*. ... Moreover, the*proof*-*relevant*version is naturally transitive, which is, somewhat notoriously, not*generally*true of ordinary*logical**relations*. ...##
###
Page 4712 of Mathematical Reviews Vol. , Issue 87i
[page]

1987
*
Mathematical Reviews
*

view on the

*relation*between*relevant*derivability and axiomatic systems*for**relevant**logics*. ... In the present paper we (i) articulate a Fitch- style system*for**relevant*E-derivability, (ii) illustrate its use, (iii)*generalize*the result to other*relevant**logics*, (iv) discuss the rela- tion between ...##
###
Using logical relevance for question answering

2007
*
Journal of Applied Logic
*

We propose a novel method of determining the appropriateness of an answer to a question through a

doi:10.1016/j.jal.2005.12.003
fatcat:entv6qanxnck5bedf45i22i6si
*proof*of*logical**relevance*rather than a*logical**proof*of truth. ... We define*logical**relevance*as the idea that answers should not be considered as absolutely true or false in*relation*to a question, but should be considered true more flexibly in a sliding scale of aptness ... Conclusion We have proposed a method of determining the appropriateness of an answer to a question through a*proof*of*logical**relevance*rather than a more traditional*logical**proof*of truth. ...##
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The use of theorem-proving techniques in question-answering systems

1968
*
Proceedings of the 1968 23rd ACM national conference on -
*

Yates

doi:10.1145/800186.810578
fatcat:hovlkc35wzfrbfutc7fxr7li2m
*for*h substantial contributions to the design and progran ming of system QA2. ... FINDR The function FINDR takes as its arguments the*name*of a*relation*and the arguments*for*that*relation*. ... INST is the*name*of the set-membership*relation*, and INCLUDE is the*name*of the set-inclusion*relation*.) ...##
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Non-Boolean classical relevant logics II: Classicality through truth-constants

2021
*
Synthese
*

I argue that this allows

doi:10.1007/s11229-021-03065-z
fatcat:ret4qhgklvhyblco7gdolyclne
*for*a new interpretation of Anderson and Belnap's take on*logical*consequence,*namely*as committing them to pluralism about*logical*consequence. ... The leitmotif of both this paper and its prequel is the*relevant*legitimacy of disjunctive syllogism.*Relevant**logics*are commonly held to be paraconsistent*logics*. ... Acknowledgements I am very grateful to the participants of the Bergen*Logic*Group and the audience of the LanCog Workshop on Substructural*Logics**for*constructive feedback. ...##
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Page 8384 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

The rule of universal

*generalization*turns into if A then FtxA and F-7tx-A. Then,*proofs**for*a few dozen theorems are given. ... ’ and other*relevant*concepts. ...##
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Hybrid Logics with Infinitary Proof Systems

2006
*
Journal of Logic and Computation
*

Although the completeness

doi:10.1093/logcom/exi086
fatcat:zhf34jp4ezeo5icrd7qp6fudoi
*proof*in [2] is very*general*, it is not applicable to non-compact modal*logics*, such as propositional dynamic*logic*(PDL), ancestral*logic*, other modal*logics*with (reflexive) ... We provide a strongly complete infinitary*proof*system*for*hybrid*logic*. This*proof*system can be extended with countably many sequents. ... Acknowledgments We would like to thank Balder ten Cate, Benedikt Löwe, Yde Venema, and two anonymous referees*for*their fruitful suggestions. ...##
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Page 4935 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

*Logic*22 (1993), no. 5, 481-511. As is well known, solutions to the basic semantic problems

*for*the majority of

*relevant*

*logics*were obtained by means of ternary

*relational*semantics. ... 4935 metaframes)

*for*which truth-definitions are given exclusively in terms of binary

*relations*. ...

##
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General information in relevant logic

2008
*
Synthese
*

In that article, we set out a formal semantics

doi:10.1007/s11229-008-9412-9
fatcat:3bo66rqvirdd5nqdrrgm4zzvly
*for*quanti...ed*relevant**logic*. 1 Here I provide a philosophical interpretation*for*that semantics. ... This paper sets out a philosophical interpretation of the model theory in Mares and Goldblatt "An Alternative Semantics*for*Quanti...ed*Relevant**Logic*" (The Journal of Symbolic*Logic*71 (2006) ). ... In order to axiomatize this*logic*, we add to the*logic*R the axiom 8xA ! (E ! A[ =x]), where x is free*for*in A, and the rule`A ! (Ex ! B) =)`A ! 8xB, where x does not occur free in A. 13 , 14 ...##
###
Page 4252 of Mathematical Reviews Vol. , Issue 85j
[page]

1985
*
Mathematical Reviews
*

Their common

*name*,*relevant**logics*, comes from the*relevance*principle that is considered to be basic in such*logics*. ... Wrightson, Graham (NZ-VCTR) 85j:03024 *On some semantic tableau*proof*procedures*for*modal*logic*. With a German summary. ...##
###
Page 208 of Mathematical Reviews Vol. 16, Issue 3
[page]

1955
*
Mathematical Reviews
*

The ideas associated with these

*names*are also,*for*the most part, lacking. ... In this book the author presents a*general*treatment of symbolic*logic*as seen from his point of view. ...##
###
Page 814 of Mathematical Reviews Vol. , Issue 81C
[page]

1981
*
Mathematical Reviews
*

*For*modal

*logics*in

*general*, | Theorem 2 remains unproven and is presumably false. The

*proof*| of Theorem 5 survives after a few changes, but Theorem 4 be comes totally problematic. ... First, many of the results quoted

*for*the

*relation*C (

*for*example, 1-9 on pp. 421 f.) are provided neither with

*proofs*nor with adequate references to

*proofs*; a compact source of most of these results ...

##
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Tarski's relevance logic; Version 2
[article]

2019
*
arXiv
*
pre-print

*For*example, the Axiom of Contraposition is not in Tarski's

*relevance*

*logic*. ... It also contains a formula (not previously known or considered as an axiom

*for*any

*relevance*

*logic*) that provides a counterexample to a completeness theorem of T. ... The formulas involved are complicated and not

*generally*considered as potential axioms

*for*

*relevance*

*logics*. Two formulas that are not theorems of R are given in [30, Theorem 8.2] . ...

##
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Relevant Connexive Logic

2019
*
Logic and Logical Philosophy
*

In this paper, a connexive extension of the

doi:10.12775/llp.2019.007
fatcat:rzwj5b2wrvcmlfpizx2sqosooq
*relevance**logic*R→ was presented. It is defined by means of a natural deduction system, and a deductively equivalent axiomatic system is presented too. ... The goal of such an extension is to produce a*logic*with stronger connection between the antecedent and the consequent of an implication. ... See [15]*for*a*general*discussion of this difference, and [3]*for*a discussion of this difference in the context of*relevance**logics*. ...
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