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Classical Resolution for Many-Valued Logics

João Marcos, Cláudia Nalon
2016 Electronical Notes in Theoretical Computer Science  
Also, the search 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  ... 
doi:10.1016/j.entcs.2016.09.001 fatcat:knq57n63gvg6rkdxe6c7s35ozy

A Resolution Method for Linguistic Many-valued Logic

Le Anh Phuong, Tran Dinh Khang
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.  ... 
doi:10.12785/amis/070343 fatcat:zsbfq3doivdqpn6eja2mhrhd3i

Resolution-based Theorem Proving for Many-valued Logics

Matthias Baaz, Christian G. Fermüller
1995 Journal of symbolic computation  
First, 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.  ... 
doi:10.1006/jsco.1995.1021 fatcat:btdei7e4rfb25mh6spgot2d7na

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.  ... 

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.”  ... 

Non-Clausal Multi-ary a-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

Yang Xu, Jun Liu, Xingxing He, Xiaomei Zhong, Shuwei Chen
2018 International Journal of Computational Intelligence Systems  
The present paper focuses on the 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).  ... 
doi:10.2991/ijcis.11.1.29 fatcat:7x6aid2wxjgedox57jy74az5sq

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

Viorica Sofronie-Stokkermans
2007 Annals of Mathematics and Artificial Intelligence  
In this context, we show that refinements of 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.  ... 
doi:10.1007/s10472-007-9051-8 fatcat:npctskj7pjayva2jzhvuldb5yq

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]

Zbigniew Stachniak
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.  ... 
doi:10.1007/978-3-540-30210-0_2 fatcat:vzlccfeqijg3tfh3v73lelk7du

Mathematical Logic and Deduction in Computer Science Education

Hashim HABIBALLA, Tibor KMET
2008 Informatics in Education. An International Journal  
Further we discuss the possibilities of inclusion the non-classical (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.  ... 
doi:10.15388/infedu.2008.05 fatcat:nuiu6olbcfe57oy5y4fzhfk2vu

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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