A temporal negative normal form which preserves implicants and implicates

ABSTRACT Most theorem provers for Classical Logic transform the input formula into a particular normal form. This tranformation is done before the execution of the algorithm (Resolution and Dissolution) or it is integrated into the deductive algorithm (Tableaux). This situation is no different for Non-Classical Logics and, particularly, for Temporal Logics ([Fis91], [Fis97], [MP95], [Wol85]). However, unlike classical logic, temporal logic does not provide an extension of the notion of non negative normal form. In this work, we define a temporal negative normal form for the future fragment of the linear time propositional temporal logic, named FNext. The definition saves as much information as possible about implicants and implicates of the input formula and its subformulas. This property is the novelty of this normal form; for example, in [Fis97] the normal form is guided by the separation property and in [Ven86] the normal form provided prepares the input formula to be treated by a resolution method. Moreover, we also introduce an algorithm having linear cost, which transforms the input formula into a temporal negative normal form. Furthermore, in this work we present a new structure and a set of operators over it that allows us to efficiently manage the information about unitary implicants and implicates contained in the subformulae.

[1]  David A. Plaisted,et al.  A Structure-Preserving Clause Form Translation , 1986, J. Symb. Comput..

[2]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

[3]  Michael Fisher,et al.  A Resolution Method for Temporal Logic , 1991, IJCAI.

[4]  Orna Grumberg,et al.  Verification of Temporal Properties , 1993, J. Log. Comput..

[5]  Mihalis Yannakakis,et al.  The complexity of probabilistic verification , 1995, JACM.

[6]  Manuel Ojeda-Aciego,et al.  TAS-D++: Syntactic Trees Transformations for Automated Theorem Proving , 1994, JELIA.

[7]  Manuel Ojeda-Aciego,et al.  Reducing signed propositional formulas , 1999, Soft Comput..

[8]  Manuel Ojeda Aciego,et al.  A reduction-based theorem prover for 3-valued logic , 1997 .

[9]  G. Venkatesh,et al.  A Decision Method for Temporal Logic Based on Resolution , 1985, FSTTCS.

[10]  Inmaculada Perez de Guzmán,et al.  A new algebraic semantic approach and some adequate connectives for computation with temporal logic over discrete time , 1992, J. Appl. Non Class. Logics.

[11]  Tsutomu Sasao,et al.  Logic Synthesis and Optimization , 1997 .

[12]  Zohar Manna,et al.  Temporal Verification of Reactive Systems , 1995, Springer New York.

[13]  Rachel Ben-Eliyahu-Zohary,et al.  A Temporal Logic for Proving Properties of Topologically General Executions , 1996, Inf. Comput..

[14]  Raymond Reiter,et al.  Characterizing Diagnoses and Systems , 1992, Artif. Intell..

[15]  Inmaculada Perez de Guzmán,et al.  Temporal Reasoning over Linear Discrete Time , 1996, JELIA.

[16]  Zohar Manna,et al.  Temporal verification of reactive systems - safety , 1995 .

[17]  Michael Fisher,et al.  A Normal Form for Temporal Logics and its Applications in Theorem-Proving and Execution , 1997, J. Log. Comput..

[18]  Anavai Ramesh.  Some applications of non clausal deduction , 1995 .

[19]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.