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Proof-Relevant Logical Relations for Name Generation [article]

Nick Benton, Martin Hofmann, Vivek Nigam
2017 arXiv   pre-print
This paper presents a direct-style model of a ν-calculus-like language with recursion using the novel framework of 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.  ... 
arXiv:1708.05193v1 fatcat:7awf2fmvqbbbllgiblm74amf3m

Proof-Relevant Logical Relations for Name Generation [chapter]

Nick Benton, Martin Hofmann, Vivek Nigam
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 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.  ... 
doi:10.1007/978-3-642-38946-7_6 fatcat:qxyfqkonajhilg4zc3pybwsehm

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

Marco De Boni
2007 Journal of Applied Logic  
We propose a novel method of determining the appropriateness of an answer to a question through a 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.  ... 
doi:10.1016/j.jal.2005.12.003 fatcat:entv6qanxnck5bedf45i22i6si

The use of theorem-proving techniques in question-answering systems

C. Cordell Green, Bertram Raphael
1968 Proceedings of the 1968 23rd ACM national conference on -  
Yates 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.)  ... 
doi:10.1145/800186.810578 fatcat:hovlkc35wzfrbfutc7fxr7li2m

Non-Boolean classical relevant logics II: Classicality through truth-constants

Tore Fjetland Øgaard
2021 Synthese  
I argue that this allows 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.  ... 
doi:10.1007/s11229-021-03065-z fatcat:ret4qhgklvhyblco7gdolyclne

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.  ... 

Hybrid Logics with Infinitary Proof Systems

Barteld Kooi, Gerard Renardel de Lavalette, Rineke Verbrugge
2006 Journal of Logic and Computation  
Although the completeness 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.  ... 
doi:10.1093/logcom/exi086 fatcat:zhf34jp4ezeo5icrd7qp6fudoi

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.  ... 

General information in relevant logic

Edwin D. Mares
2008 Synthese  
In that article, we set out a formal semantics 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  ... 
doi:10.1007/s11229-008-9412-9 fatcat:3bo66rqvirdd5nqdrrgm4zzvly

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  ... 

Tarski's relevance logic; Version 2 [article]

Roger D. Maddux
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] .  ... 
arXiv:1901.06567v2 fatcat:wdbky3c7vrcfncj3ktgddr34re

Relevant Connexive Logic

Nissim Francez
2019 Logic and Logical Philosophy  
In this paper, a connexive extension of the 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.  ... 
doi:10.12775/llp.2019.007 fatcat:rzwj5b2wrvcmlfpizx2sqosooq
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