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Abstract effects and proof-relevant logical relations

Nick Benton, Martin Hofmann, Vivek Nigam
2014 Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14  
The transition to proof-relevance solves two awkward problems caused by naïve use of existential quantification in Kripke logical relations, namely failure of admissibility and spurious functional dependencies  ...  Our semantics uses a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proof-relevant generalisation thereof  ...  Acknowledgments We thank Lennart Beringer and Andrew Kennedy for fruitful discussions. Nigam was supported by CAPES / CNPq and DAAD.  ... 
doi:10.1145/2535838.2535869 dblp:conf/popl/Benton0N14 fatcat:qxxlg2mvfzfbjhvl5pqgci3dra

Abstract Effects and Proof-Relevant Logical Relations [article]

Nick Benton, Martin Hofmann, Vivek Nigam
2012 arXiv   pre-print
The transition to proof-relevance solves two well-known problems caused by the use of existential quantification over future worlds in traditional Kripke logical relations: failure of admissibility, and  ...  We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proof-relevant generalisation thereof, namely  ...  In Section 5 we describe proof-relevant logical relations, prove the fundamental theorem and define observational equivalence.  ... 
arXiv:1212.5692v1 fatcat:45hejd5x4ndodask5skqem6dti

A non-transitive relevant implication corresponding to classical logic consequence

Peter Verdée, Inge De Bal, Aleksandra Samonek
2019 The Australasian Journal of Logic  
Subsequently we apply this denition to the classical logic (CL) consequence relation to obtain NTR-consequence, i.e. the relevant CL-consequence relation in our sense, and develop a sequent calculus that  ...  The object language implication reflects exactly the NTR-consequence relation. One can see the resulting logic NTR-> as a relevant logic in the traditional sense of the word.  ...  ; 3,5 In this proof all the premises are effectively used to obtain the conclusion.  ... 
doi:10.26686/ajl.v16i2.5273 fatcat:hzhd3ej365bezedb2pbzoqxuju

Relevant Consequence Relations: An Invitation [article]

Guillermo Badia, Petr Cintula, Libor Behounek, Andrew Tedder
2022 arXiv   pre-print
We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance.  ...  We motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided  ...  Acknowledgements Libor Běhounek and Petr Cintula were supported by the Czech Science Foundation project GA22-01137S. Petr Cintula was also supported by RVO 67985807.  ... 
arXiv:2207.03892v1 fatcat:jbxerzuar5dozovttgo7zu7jq4

Page 3543 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
We show some examples of relatedness relations and how they can be obtained. 03B General logic 2004e:03036 “We present an algorithm to retrieve the most relevant beliefs from a structured belief base and  ...  Kuznetsov and A. Yu. Muravitsky, “Logic of provability”, in The Fourth All-Soviet Conference on Mathematical Logic. Abstracts (Russian), 73; per revr.].  ... 

Automatic Abstraction without Counterexamples [chapter]

Kenneth L. McMillan, Nina Amla
2003 Lecture Notes in Computer Science  
The performance of this approach on benchmarks derived from microprocessor verification indicates that SAT solvers are quite effective in eliminating logic that is not relevant to a given property.  ...  A method of automatic abstraction is presented that uses proofs of unsatisfiability derived from SAT-based bounded model checking as a guide to choosing an abstraction for unbounded model checking.  ...  What these data clearly show is that the SAT solver is effective at isolating the part of the logic that is relevant to the given property, at least in the case when this part of the logic is relatively  ... 
doi:10.1007/3-540-36577-x_2 fatcat:e64cd34ovbgwpg3y37aafo5jfe

CHR: A Constructive Relevant Natural-deduction Logic

Neil Leslie, Edwin D Mares
2004 Electronical Notes in Theoretical Computer Science  
In this paper we develop a natural-deduction logic which is both constructive and relevant. We use a proof-theoretic argument to justify the rules of the logic.  ...  The system we have produced is clear and simple. The proof rules are natural to use, as we have shown in examples. We have outlined how this logic relates to other relevant logics.  ...  we outline a proof that CHR is a relevant logic in the sense of Anderson and Belnap [1] .  ... 
doi:10.1016/j.entcs.2003.12.011 fatcat:gxhkdd3orbc2bgnxyohmrkzhla

Theorem proving for untyped constructive -calculus: implementation and application

A Ramsay
2001 Logic Journal of the IGPL  
logic and the λ-calculus).  ...  The paper presents the basic theorem prover, which is a higher-order extension of Manthey and Bry's model generation theorem prover for first-order logic [14] ; considers issues relating to the compile-time  ...  Turner's analysis involves taking a classical treatment of first-order logic and adding λ-abstraction and β-reduction to it (or at any rate, operations which look extremely like λ-abstraction and β-reduction  ... 
doi:10.1093/jigpal/9.1.83 fatcat:w2aujrd5jrfq3ljpofvl7scqne

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  ...  Apart from providing a fresh solution to an old problem, this work provides an accessible setting in which to introduce the use of proof-relevant logical relations, free of the additional complexities  ...  In the context of our on-going research on the semantics of effect-based program transformations [BKHB06] , we have been led to develop proof-relevant logical relations [BHN14] .  ... 
doi:10.1007/978-3-642-38946-7_6 fatcat:qxyfqkonajhilg4zc3pybwsehm

Agenda control for heterogeneous reasoners

Reinhard Stolle, Apollo Hogan, Elizabeth Bradley
2005 The Journal of Logic and Algebraic Programming  
In particular, we describe a logic programming system that is based on three ideas: equivalence of declarative and operational semantics, declarative specification of control information, and smoothness  ...  Knowledge that has been derived in the course of the current inference process can at any time be passed to non-logic-based program modules.  ...  Acknowledgements Matt Easley and Tom Wrensch contributed ideas and code to this project.  ... 
doi:10.1016/j.jlap.2003.07.001 fatcat:txptaxp6zvd4pfgqvuhj6oapkm

Page 1596 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
This relation of cause and effect is linked to the execution of the program. Thus it is a temporal relation.  ...  Summary: “In this paper we show how to represent syntactically the relation of cause and effect between a predicate name and the bodies of the clauses which define this predicate in a logic program.  ... 

Relevant First-Order Logic LP# and Curry's Paradox Resolution

Jaykov Foukzon
2015 Pure and Applied Mathematics Journal  
In this article the non-classical resolution of Curry's Paradox and Shaw-Kwei paradox without rejection any contraction postulate is proposed.  ...  In 1942 Haskell B.Curry presented what is now called Curry paradox which can be found in a logic independently of its stand on negation.In recent years there has been a revitalised interest in non-classical  ...  A transitive relation of consequence: we write this by ⊢ and take ⊢ tobe a relation between statements, and we require that it be transitive: if ⊢ and ⊢ then ⊢ .  ... 
doi:10.11648/j.pamj.s.2015040101.12 fatcat:fzmy7dpojvdphiqr2rznamgpka

How Formal Logic Can Fail to Be Useful for Modelling or Designing MAS [chapter]

Bruce Edmonds
2004 Lecture Notes in Computer Science  
particular cases, but where the logic is not actually used to make any substantial inferences and no application of the logic demonstrated.  ...  I counter the argument that theory is necessary by denying that the theory has to be so abstract.  ...  Logics in this vein included intuitionistic logic, free logic, relevance logic and modal logic.  ... 
doi:10.1007/978-3-540-25867-4_1 fatcat:5vu2kzvgofdi3ezqoeyryuvnsm

How Formal Logic Can Fail to be Useful for Modelling or Designing MAS

Bruce Edmonds
2003 Social Science Research Network  
particular cases, but where the logic is not actually used to make any substantial inferences and no application of the logic demonstrated.  ...  I counter the argument that theory is necessary by denying that the theory has to be so abstract.  ...  Logics in this vein included intuitionistic logic, free logic, relevance logic and modal logic.  ... 
doi:10.2139/ssrn.327320 fatcat:yd4hyjip2jfhbok2w3gbyh2nru

A Paraconsistent Decagon

João Marcos, Diderik Batens, Walter Carnielli
2005 Journal of Applied Logic  
the classical paradigm many desirable features, as model existence results and model theory, reasonable proof methods, algebraic and set-theoretic counterparts, (un)decidability and so on.  ...  Much of the impetus of the research on paraconsistent logics is motivated by the attainment of those goals: Taming the explosive power of contradictions, and yet being able to deliver logics sharing with  ...  This logic combines classical logic with relevance logics and paraconsistent logics in da Costa's style.  ... 
doi:10.1016/j.jal.2004.07.008 fatcat:tbuc2kgjs5hyvokunioqhbhlp4
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