Uniform and Non Uniform Strategies for Tableaux Calculi for Modal Logics

ABSTRACT The major emphasis of this paper is on the definition of complete strategies in tableaux calculi for propositional modal logics. The strategies use a non exhaustive backtracking mechanism, a selective periodicity test and a uniform or a non uniform priority on the order of application of the tableaux rules. The propositional modal logics treated herein are those having a tableaux calculus with finite sets of formulas possibly occurring in the tableaux. Experimental results with the ATINF modal prover are presented.

[1]  Ricardo Caferra,et al.  A Generic Graphic Framework for Combining Inference Tools and Editing Proofs and Formulae , 1994, J. Symb. Comput..

[2]  Stéphane Demri Efficient Strategies for Automated Reasoning in Modal Logics , 1994, JELIA.

[3]  Fabio Massacci,et al.  Strongly Analytic Tableaux for Normal Modal Logics , 1994, CADE.

[4]  Zoran Ognjanovic A Tableau-Like Proof Procedure for Normal Modal Logics , 1994, Theor. Comput. Sci..

[5]  S. Demri Approches directe et par traduction en logiques modales: nouvelles stratégies et traduction inverse de preuves , 1994 .

[6]  Hans de Nivelle Generic Resolution in Propositional Modal Systems , 1993, LPAR.

[7]  Andrei Voronkov,et al.  Theorem Proving in Non-Standard Logics Based on the Inverse Method , 1992, CADE.

[8]  Lincoln A. Wallen,et al.  Automated deduction in nonclassical logics , 1990 .

[9]  T. Käufl,et al.  Cooperation of decision procedures in a tableau-based theorem prover , 1990 .

[10]  James P. Delgrande,et al.  Tableau-Based Theorem Proving In Normal Conditional Logics , 1988, AAAI.

[11]  Hans Jürgen Ohlbach,et al.  A Resolution Calculus for Modal Logics , 1988, CADE.

[12]  Michael A. McRobbie,et al.  The KRIPKE Automated Theorem Proving System , 1986, CADE.

[13]  Luis Fariñas del Cerro,et al.  Un Principe de Résolution en Logique Modale , 1984, RAIRO Theor. Informatics Appl..

[14]  Alan Bundy,et al.  The Computer Modelling of Mathematical Reasoning , 1983 .

[15]  Wolfgang Rautenberg,et al.  Modal tableau calculi and interpolation , 1983, J. Philos. Log..

[16]  Drew McDermott,et al.  Nonmonotonic Logic II: Nonmonotonic Modal Theories , 1982, JACM.

[17]  Vaughan R. Pratt,et al.  Application of modal logic to programming , 1980 .

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

[19]  Gerald J. Massey Binary closure-algebraic operations that are functionally complete , 1970, Notre Dame J. Formal Log..

[20]  Boleslaw Sobocinski Note on G. J. Massey's closure-algebraic operation , 1970, Notre Dame J. Formal Log..

[21]  R. Smullyan First-Order Logic , 1968 .

[22]  J. Hintikka Knowledge and belief , 1962 .

[23]  Alfred Tarski,et al.  Some theorems about the sentential calculi of Lewis and Heyting , 1948, The Journal of Symbolic Logic.