Monodic Temporal Resolution

First-order temporal logic is a coincise 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 have identified important enumerable and even decidable fragments. In this paper we present the first resolution-based calculus for monodic first-order temporal logic. Although the main focus of the paper is on establishing completeness result, we also consider implementation issues and define a basic loop-search algorithm that may be used to guide the temporal resolution system.

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.

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.