Inman P. de Guzmán

Temporal Reasoning over Linear Discrete Time

In this work we present a new Automated Theorem Prover, called TAS-FNext, applied to temporal logic. This is part of a broader project developed by our research group GIMAC. It is an extension of works [4], [5] and [6] concerns classical logic and [9] Minimal Temporal Logic.

Reduction Theorems for Boolean Formulas Using Delta-Trees

A new tree-based representation for propositional formulas, named Δ-tree, is introduced. Δ-trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem.

A new algebraic semantic approach and some adequate connectives for computation with temporal logic over discrete time

ABSTRACT In this paper we present a new semantic approach for propositional linear temporal logic with discrete time, strongly based in the well-order of IN (the set of natural numbers). We consider temporal connectives which express precedence, posteriority and simultaneity, and they provide a family of expressively complete temporal logics. The selection of the new semantics and connectives used in this work was principally to obtain a suitable executable temporal logic, which can be used for the specification and control of process behaviour in discrete time in a similar way to thai presented by D. Gabbay in [GAB 89], Our new approach has two advantages: firstly, the connectives are defined intuitively so that they have interpretations which relate to properties of interest in real systems; secondly, it provides a new semantics that facilitates simpler proofs of many valid formulas and metatheorems. To confirm this second advantage, we use our semantics to give a formal proof of the Separation Theorem ...

A functional approach for temporal × modal logics

Abstract. This work is focused on temporal

TAS-D++: Syntactic Trees Transformations for Automated Theorem Proving

\times

Restricted Delta-Trees and Reduction Theorems in Multiple-Valued Logics

modal logics. We study the representation of properties of functions of interest because of their possible computational interpretations. The semantics is exposed in an algebraic style, and the definability of the basic properties of the functions is analysed. We introduce minimal systems for linear time with total functions as well as with a class of partial functions (those with uniform domain). Moreover, completeness proofs are offered for these minimal systems. Finally, functional-validity is compared with

Structure Theorems for Closed Sets of Implicates/ Implicants in Temporal Logic

T\times W

A Temporal × Modal Approach to the Definability of Properties of Functions

-validity and Kamp-validity.

Implicates and Reduction Techniques for Temporal Logics

In this work a new Automated Theorem Prover (ATP) via refutation for classical logic and which does not require the conversion to clausal form, named TAS-D++, is introduced. The main objective in the design of this ATP was to obtain a parallel and computationally efficient method naturally extensible to non-standard logics (concretely, to temporal logics, see [8]).

Proceedings of the European Workshop on Logics in Artificial Intelligence

In this paper we continue the theoretical study of the possible applications of the ?-tree data structure for multiple-valued logics, specifically, to be applied to signed propositional formulas. The ?-trees allow a compact representation for signed formulas as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. New and improved versions of reduction theorems for finite-valued propositional logics are introduced, and a satisfiability algorithm is provided which further generalise the TAS method [1,5].