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

@inproceedings{Fisher1996ARP,
  title={A Resolution-Based Proof Method for Temporal Logics of Knowledge and Belief},
  author={Michael Fisher and Michael Wooldridge and Clare Dixon},
  booktitle={FAPR},
  year={1996}
}
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… 

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References

SHOWING 1-10 OF 31 REFERENCES

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