Towards the Implementation of First-Order Temporal Resolution: the Expanding Domain Case

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. In this paper, we develop a clausal resolution method for the monodic fragment of first-order temporal logic over expanding domains. We first define a normal form for monodic formulae and then introduce novel resolution calculi that can be applied to formulae in this normal form. We state correctness and completeness results for the method. We illustrate the method on a comprehensive example. The method is based on classical first-order resolution and can, thus, be efficiently implemented.

Searching for Invariants Using Temporal Resolution

In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising a wide class of temporal problems. We demonstrate that this scheme of searching for invariants can be also applied to a class of multi-predicate induction problems represented by mutually recursive definitions. Completeness of the approach, examples of the application of the scheme, and overview of the implementation are described.

A Simplified Clausal Resolution Procedure for Propositional Linear-Time Temporal Logic

The clausal resolution method for propositional linear-time temporal logic is well known and provides the basis for a number of temporal provers. The method is based on an intuitive clausal form, called SNF, comprising three main clause types and a small number of resolution rules. In this paper, we show how the normal form can be radically simplified, and consequently, how a simplified clausal resolutioin method can be defined for this impoprtant variety of logics.

Equality and Monodic First-Order Temporal Logic

It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.

Towards First-Order Temporal Resolution

In this paper we show how to extend clausal temporal resolution to the ground eventuality fragment of monodic first-order temporal logic, which has recently been introduced by Hodkinson, Wolter and Zakharyaschev. While a finite Hilbert-like axiomatization of complete monodic first order temporal logic was developed by Wolter and Zakharyaschev, we propose a temporal resolution-based proof system which reduces the satisfiability problem for ground eventuality monodic first-order temporal formulae to the satisfiability problem for formulae of classical first-order logic.