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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.  ...

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.  ...

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.  ...

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.)  ...

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.  ...

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  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.  ...

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  ...

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  ...