Automated Reasoning Algorithm for Linguistic Valued Lukasiewicz Propositional Logic

In this paper, firstly a new automated reasoning algorithm based on Boolean logic is proposed and its theorems of soundness and completeness on validating the unsatisfiability of logic formulae are given. Then this procedure is extended to a linguistic valued Lukasiewicz propositional logic L(X) with truth-value in Lukasiewicz linguistic valued algebras, and an a- automated reasoning algorithm with respect to certain linguistic value level a in L(X) is given. Its theorems of soundness and completeness associated with the a- unsatisfiability of the logical formulae in L(X) are also proved. This reflects the symbolic approach acts by direct reasoning on linguistic truth values.

[1]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[2]  Reiner Hähnle,et al.  Automated deduction in multiple-valued logics , 1993, International series of monographs on computer science.

[3]  Etienne E. Kerre,et al.  alpha-Resolution principle based on first-order lattice-valued logic LF(X) , 2001, Inf. Sci..

[4]  Stephan Lehmke.  A Resolution-Based Axiomatisation of ‘Bold’ Propositional Fuzzy Logic , 1999 .

[5]  N. C. Ho,et al.  Hedge algebras: an algebraic approach to structure of sets of linguistic truth values , 1990 .

[6]  Lawrence J. Henschen,et al.  The Completeness of GP-Resolution for Annotated Logics , 1992, Inf. Process. Lett..

[7]  Etienne E. Kerre,et al.  alpha-Resolution principle based on lattice-valued propositional logic LP(X) , 2000, Inf. Sci..

[8]  Jun Liu,et al.  A resolution-like strategy based on a lattice-valued logic , 2003, IEEE Trans. Fuzzy Syst..

[9]  V. S. Subrahmanian,et al.  Theory of Generalized Annotated Logic Programming and its Applications , 1992, J. Log. Program..

[10]  Harald Ganzinger,et al.  Chaining techniques for automated theorem proving in many-valued logics , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[11]  Jan Pavelka,et al.  On Fuzzy Logic II. Enriched residuated lattices and semantics of propositional calculi , 1979, Math. Log. Q..

[12]  Didier Dubois,et al.  Resolution principles in possibilistic logic , 1990, Int. J. Approx. Reason..

[13]  N. C. Ho,et al.  Extended hedge algebras and their application to fuzzy logic , 1992 .

[14]  V. S. Subrahmanian,et al.  Paraconsistent Logic Programming , 1987, FSTTCS.

[15]  Peter H. Schmitt,et al.  Computational Aspects of Three-Valued Logic , 1986, CADE.

[16]  Jang-Suk Park,et al.  A new fuzzy resolution principle based on the antonym , 2000, Fuzzy Sets Syst..

[17]  Thomas Weigert,et al.  Fuzzy operator logic and fuzzy resolution , 1993, Journal of Automated Reasoning.

[18]  Zbigniew Stachniak.  Resolution proof systems - an algebraic theory , 1996, Automated reasoning series.

[19]  V. Novák.  Fuzzy sets and their applications , 1989 .

[20]  J. A. Goguen,et al.  The logic of inexact concepts , 1969, Synthese.

[21]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[22]  E. Turunen.  Algebraic structures in fuzzy logic , 1992 .

[23]  Nicola Olivetti,et al.  Resolution and Model Building in the Infinite-Valued Calculus of Lukasiewicz , 1998, Theor. Comput. Sci..

[24]  Alan Robinson,et al.  Handbook of automated reasoning , 2001 .

[25]  Christian G. Fermüller,et al.  Resolution for Many-Valued Logics , 1992, LPAR.

[26]  Zbigniew Stachniak.  Resolution Proof Systems , 1996, Automated Reasoning Series.

[27]  Richard C. T. Lee.  Fuzzy Logic and the Resolution Principle , 1971, JACM.