Deduction by combining semantic tableaux and integer programming

. In this paper we propose to extend the current capabilities of automated reasoning systems by making use of techniques from integer programming. We describe the architecture of an automated reasoning system based on a Herbrand procedure (enumeration of formula instances) on clauses. The input are arbitrary sentences of first-order logic. The translation into clauses is done incrementally and is controlled by a semantic tableau procedure using unification. This amounts to an incremental polynomial CNF transformation which at the same time encodes part of the tableau structure and, therefore, tableau-specific refinements that reduce the search space. Checking propositional unsatisfiability of the resulting sequence of clauses can either be done with a symbolic inference system such as the Davis-Putnam procedure or it can be done using integer programming. If the latter is used a number of advantages become apparent. Introduction In this paper we propose to extend the current capabilit..

Labelled Tableaux for Distributed Temporal Logic

The distributed temporal logic DTL is a logic for reasoning about temporal properties of discrete distributed systems from the local point of view of the system's agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labelled tableaux system for full DTL. To achieve this, we first formalize a labelled tableaux system for reasoning locally at each agent and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL. We also provide examples illustrating the use of DTL and our tableaux syste

A general tableau method for propositional interval temporal logics: Theory and implementation

In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema’s CDT logic interpreted over partial orders (BCDT+ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented

Improving Temporal Logic Tableaux using Integer Constraints

Introduction In this position paper we present some ideas that aim to improve analytic tableau for temporal logics with the ultimate goal of reviving the interest in using them for temporal logic satisfiability checking. Although tableau formulations for several propositional temporal logics exist [9], these are not used much in practice, because the tableau size becomes intractable already for quite small formulas. Moreover, checking tableau closure is complicated and expensive to implement. For practical purposes, usually automata theoretic approaches are preferred [3]. It might, however, still be interesting to have competitive tableau formulations as will be pointed out in Section 4. The ideas for the research reported here were stimulated by [6, 7] where an extension of analytic tableau with linear constraints led to an efficient (mixed) integer programming formulation of a tableau system for finitely and infinitelyvalued propositional logics. The usefulness of linear co