A Resolution-Based Proof Method for Temporal Logics of Knowledge and Belief

  title={A Resolution-Based Proof Method for Temporal Logics of Knowledge and Belief},
  author={Michael Fisher and Michael Wooldridge and Clare Dixon},
In this paper we define two logics, KLn and BLn, and present resolution-based proof methods for both. KLn is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BLn is somewhat similar: it is a temporal logic that contains connectives for representing the beliefs of agents. The proof methods we present for these logics involve two… 

A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief

This paper defines two logics, KLn and BLn, and presents tableau-based decision procedures for both and includes a brief review of their applications in AI and mainstream computer science.

A Tableau Calculus for Temporal Description Logic: the Expanding Domain Case

This paper provides a new method of how tableau-based decision procedures can be constructed for many-dimensional logics which lack the nite model property, and can be applied to deal with other temporalized formalisms as well.

A Mechanisation of Classical Modal Tense Logics Using Isabelle

  • J. DawsonR. Goré
  • Computer Science
    Australian Joint Conference on Artificial Intelligence
  • 1998
This work presents an implementation of an interactive theorem prover for the basic tense logic K t, and many of its extensions, using the generic proof assistant Isabelle, using a Display Logic formalism of K t as opposed to a traditional Gentzen system.

Resolution-based proof for multi-modal temporal logics of knowledge

  • C. DixonMichael Fisher
  • Philosophy
    Proceedings Seventh International Workshop on Temporal Representation and Reasoning. TIME 2000
  • 2000
This paper presents a resolution method for propositional temporal logic combined with multi-modal S5 and illustrates its use on examples.

Resolution for Temporal Logics of Knowledge

A resolution based proof system for a temporal logic of knowledge is given and shown to be correct and useful for proving properties of distribut ed and multi-agent systems.

A resolution method for CTL branching-time temporal logic

  • A. BolotovMichael Fisher
  • Philosophy
    Proceedings of TIME '97: 4th International Workshop on Temporal Representation and Reasoning
  • 1997
The clausal resolution method for linear temporal logics is extended to a branching-time framework and the key elements of the resolution method, namely the normal form, the concept of step resolution and a novel temporal resolution rule, are introduced and justified.

A Knowledge-Theoretic Semantics for Concurrent METATEM

The aim of this paper is to develop a semantics for the multi-agent programming language Concurrent MetateM, by using the tools of knowledge theory, and shows that certain formulae of this logic correspond to properties of ConcurrentmetateM systems.

The Set of Support strategy in temporal resolution

  • C. DixonMichael Fisher
  • Computer Science
    Proceedings. Fifth International Workshop on Temporal Representation and Reasoning (Cat. No.98EX157)
  • 1998
This work introduces, justifies and applies a temporal version of the 'Set of Support' strategy, thus allowing the supporting set to be carried over between the different phases of the resolution method, and retains the completeness of the refutation process.

Towards formal methods for agent-based systems

This paper considers how formal methods might be developed for use in agent-based systems and presents an approach based upon the description of agents using temporal specifications, which can be executed directly to provide the behaviour of an individual agent or collections of such descriptions under a specific operational model.

Complete Axiomatizations for Logics of Knowledge and Past Time ( Long Version )

Sound and complete axiomatizations are provided for two different logics involving modalities for knowledge and both past and future time modalities. The logics considered allow for multiple agents



A Graph-Based Approach to Resolution in Temporal Logic

Algorithms developed in order to implement a clausal resolution method for discrete, linear temporal logics and have been combined with sub-programs performing translation to normal form and non-temporal resolution to produce an integrated resolution based temporal theorem-prover.

Temporal and Modal Logic

  • E. Emerson
  • Philosophy
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990

A Resolution Method for Temporal Logic

The resolution method is based on classical resolution, but incorporates a temporal resolution rule that can be implemented efficiently using a graph-theoretic approach.

A Decision Procedure for a Temporal Belief Logic

A tableau-based decision procedure for \(\mathcal{L}_{TB}\) is described, and some examples of its use are presented, and the paper concludes with a discussion and future work proposals.

A Normal Form for First-Order Temporal Formulae

This paper introduces a first-order temporal logic, based on a linear discrete model structure, and the procedure for transforming an arbitrary formula of this logic to First-Order Separated Normal Form (SNFf), which forms the basis of both a temporal resolution method and a family of executable temporal logics.

What can machines know?: On the properties of knowledge in distributed systems

A formal model is presented in which one can capture various assumptions frequently made about systems, such as whether they are deterministic or nondeterministic, whether knowledge is cumulative, and whether or not the "environment" affects the state transitions of the processes.

Knowledge, Belief and Time