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Classical Resolution for Many-Valued Logics

2016
*
Electronical Notes in Theoretical Computer Science
*

Also, the search

doi:10.1016/j.entcs.2016.09.001
fatcat:knq57n63gvg6rkdxe6c7s35ozy
*for*inconsistency (in the language of a given*many*-*valued**logic*) takes the form of hyper-*resolution*inference rules in the classical metalanguage, allowing*for*a uniform classic-like approach ... In contrast to previous approaches to the same problem, our target language is fully classical, what turns the design of the*resolution*-based rules*for*a specific*many*-*valued**logic*into a straightforward ... Briefly, both of the latter papers present clausal*resolution*-based procedures, taking as inputs a formula in the language of a particular*many*-*valued**logic*and transforming it into a Every*Many*-*valued*...##
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A Resolution Method for Linguistic Many-valued Logic

2013
*
Applied Mathematics & Information Sciences
*

*value*domain (AX), in an attempt to propose a general

*resolution*

*for*linguistic

*many*-

*valued*

*logic*based on hedge moving rules and linguistic lukasiewicz algebra

*for*linguistic reasoning. ... Its theorems of soundness and completeness associated with general

*resolution*are also proved. This reflects the symbolic approach acts by direct reasoning on linguistic truth

*value*domain. ... Acknowledgement The authors would like to express deep gratitude to Vietnam's National Foundation

*for*Science and Technology Development (NAFOSTED)

*for*its support. ...

##
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Resolution-based Theorem Proving for Many-valued Logics

1995
*
Journal of symbolic computation
*

First,

doi:10.1006/jsco.1995.1021
fatcat:btdei7e4rfb25mh6spgot2d7na
*logic*-speci c translation calculi are used to generate clause forms*for*arbitrary formulas of a*many*-*valued**logic*. ... A general approach to automated theorem proving*for*all rst-order nite-*valued**logics*that can be de ned truth-functionally is described. ... This allows to transfer to*many**valued*clause*logic**many*re nements of*resolution*that are essential*for*e cient theorem proving. ...##
###
Page 3067 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

(A-TUWN-CL,; Vienna)

*Resolution**for**many*-*valued**logics*. (English summary)*Logic*programming and automated reasoning (St. Petersburg, 1992), 107-118, Lecture Notes in Comput. ... Summary: “To achieve efficient proof procedures*for*quantifica- tional*logics*with finitely*many*truth*values*we extend the classical*resolution*principle. ...##
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Page 3545 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

Summary: “In this paper we present a

*resolution*method*for*the*many*-*valued*mixed Post*logic*PostL introduced by Kosovskii and Tishkov. ... Compared to related approaches, our*resolution*method leads in*many*cases to a reduction of the number of clauses that are generated. We prove soundness and completeness of*resolution**for*PostL.” ...##
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Non-Clausal Multi-ary a-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

2018
*
International Journal of Computational Intelligence Systems
*

The present paper focuses on the

doi:10.2991/ijcis.11.1.29
fatcat:7x6aid2wxjgedox57jy74az5sq
*resolution*-based automated reasoning theory in a*many*-*valued**logic*with truth-*values*defined in a lattice-ordered*many*-*valued*algebraic structure -lattice implication algebras ... is introduced*for*a lattice-*valued*propositional*logic*LP(X) based on LIA, which is essentially a non-clausal generalized*resolution*avoiding reduction to normal clausal form. ... Acknowledgments This work is supported by the National Science Foundation of China (Grant No. 61673320) and the Fundamental Research Funds*for*the Central Universities (Grant No. 2682017ZT12). ...##
###
Page 7150 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

*Logic*Comput. 4 (1994), no. 6, 905-927. From the summary: “

*Many*successfui theorem-proving methods in two-

*valued*

*logic*, notably

*resolution*, presume the existence of a conjunctive normal form (CNF). ... We discuss several possible

*resolution*rules that operate on the signed CNF including a streamlined version

*for*so-called regular

*logics*, a class of finitely

*valued*

*logics*that 03 MATHEMATICAL

*LOGIC*AND ...

##
###
Page 6062 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

Lukasiewicz’s continuously

*many*-*valued*propositional*logic*L..; in particular, we sketch the development of a structure- preserving clausal form*for*this*logic*, define*resolution*-based rules of inference ... Lukasiewicz’s*many*-*valued**logic*can be algebraically described by an algebra 4 =(M,:{1},~,—) and Gédel’s*many*-*valued**logic*corresponds to an algebra WY" = (M,;{1},7,=>,/ M,, is the set l —2 0, ——, Rae ...##
###
Page 7666 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

The method provides a new original viewpoint on finite

*many*-*valuedness*. Indeed, we present a uniform modal encoding of any finite*many*-*valued**logic*that views truth-*values*as nominals. ... Summary: “We present a method*for*testing validity*for*any finite*many*-*valued**logic*by using simple transformations into the validity problem*for*von Wright’s*logic*of elsewhere. ...##
###
Automated theorem proving by resolution in non-classical logics

2007
*
Annals of Mathematics and Artificial Intelligence
*

In this context, we show that refinements of

doi:10.1007/s10472-007-9051-8
fatcat:npctskj7pjayva2jzhvuldb5yq
*resolution*can often be used successfully*for*automated theorem proving, and in*many*interesting cases yield optimal decision procedures. ... This paper is an overview of a variety of results, all centered around a common theme, namely embedding of non-classical*logics*into first order*logic*and*resolution*theorem proving. ... Several papers on*many*-*valued**logics*present methods*for*automated theorem proving which are similar to classical*resolution*. ...##
###
Page 1596 of Mathematical Reviews Vol. , Issue 93c
[page]

1993
*
Mathematical Reviews
*

*many*-

*valued*first-order

*logic*that con- structs its minimal

*resolution*approximation, i.e. an approximation class consisting of

*resolution*proof systems of the smallest sizes possible. ... Therefore, it is necessary to introduce finitely

*many*truth

*values*. ...

##
###
Page 2799 of Mathematical Reviews Vol. , Issue 82g
[page]

1982
*
Mathematical Reviews
*

Turquette [

*Many*-*valued**logics*, North-Holland, Amsterdam, 1951; MR 14, 526]. The result is applied to n-*valued*Lukasiewicz calculi. ... {Reviewer’s remark: Interpolation theorems*for**many*-*valued*predicate and propositional*logics*have been given by a number of authors [see,*for*example, H. Rasiowa, Bull. Acad. Polon. Sci. Ser. Sci. ...##
###
Finite Algebras and AI: From Matrix Semantics to Stochastic Local Search
[chapter]

2004
*
Lecture Notes in Computer Science
*

*For*

*many*

*resolution*

*logics*the tautology problem is coNP-complete. ... In AI, matrix semantics (and a closely related discipline of

*many*-

*valued*

*logics*) has been successfully exploited in the areas of Automated Reasoning, KRR, and

*Logic*Programming (cf. ...

##
###
Mathematical Logic and Deduction in Computer Science Education

2008
*
Informatics in Education. An International Journal
*

Further we discuss the possibilities of inclusion the non-classical (

doi:10.15388/infedu.2008.05
fatcat:nuiu6olbcfe57oy5y4fzhfk2vu
*many*-*valued*)*logics*in education together with the original generalization of the non-clausal*resolution*rule into fuzzy*logic*. ... Although in tertiary level computer science education it has a solid place, it does not hold also*for*secondary level education. ...*Logic*and Knowledge Representation in CSE The classical (two-*valued*)*logic*is a formalism known*for**many*years. ...##
###
Page 2866 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

Using these results on unfolding

*many*-*valuedness*, we then give*many*-*valued*fixpoint characterizations*for*the set of all minimal models and the least model state. ... Thus, existing technology*for*classical disjunctive*logic*program- ming can be used to implement*many*-*valued*disjunctive*logic*programming. ...
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