A Relational Formalisation of Arbitrary Finite Valued Logics

A method of developing a relational semantics and relational proof systems for many-valued logics based on finite algebras of truth values is presented. The method is applied to Rosser-Turquette logic, logics based on symmetric Heyting algebras with operators and a Post-style logic.

[1]  Marcelo F. Frias,et al.  Equational Reasoning in Non--Classical Logics , 1998, J. Appl. Non Class. Logics.

[2]  Melvin Fitting,et al.  Many-valued modal logics , 1991, Fundam. Informaticae.

[3]  Walter Alexandre Carnielli,et al.  Systematization of finite many-valued logics through the method of tableaux , 1987, Journal of Symbolic Logic.

[4]  Szabolcs Mikulás,et al.  Lambek Calculus and its relational semantics: Completeness and incompleteness , 1994, J. Log. Lang. Inf..

[5]  Charles G. Morgan,et al.  Local and global operators and many-valued modal logics , 1979, Notre Dame J. Formal Log..

[6]  Ewa Orlowska,et al.  Relational Semantics for Nonclassical Logics: Formulas are Relations , 1994 .

[7]  Beata Konikowska,et al.  A Logic for Reasoning about Relative Similarity , 1997, Stud Logica.

[8]  Charles G. Morgan,et al.  Many-valued propositional intuitionism , 1976 .

[9]  Wendy MacCaull Relational Proof System for Linear and Other Substructural Logics , 1997, Log. J. IGPL.

[10]  Helena Rasiowa,et al.  Plain Semi-Post algebras as a poset-based generalization of post algebras and their representability , 1989, Stud Logica.

[11]  Marcelo F. Frias,et al.  A proof system for fork algebras and its applications to reasoning in logics based on intuitionism , 1995 .

[12]  Charles G. Morgan,et al.  Methods for Automated Theorem Proving in Nonclassical Logics , 1976, IEEE Transactions on Computers.

[13]  A. R. Turquette,et al.  On the Many-Valued Logics , 1941 .

[14]  Luisa Iturrioz Symmetrical Heyting Algebras with Operators , 1983, Math. Log. Q..

[15]  Melvin Fitting,et al.  Many-valued modal logics II , 1992 .

[16]  S. K. Thomason Possible worlds and many truth values , 1978 .

[17]  stanisław j. surma,et al.  an algorithm for axiomatizing every finite logic**The paper was presented at the International Symposium on Multiple-Valued Logic, Morgantown, West Virginia, U.S.A., May, 1974. An abstract of this paper is published in [3]. , 1977 .

[18]  Luisa Iturrioz Modal operators on symmetrical Heyting algebras , 1982 .

[19]  Wendy MacCaull,et al.  Relational semantics and a relational proof system for full Lambek calculus , 1998, The Journal of Symbolic Logic.