Abstract
In this paper we define two logics, KL n and BL n, and present resolution-based proof methods for both. KL n 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 BL n 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 key steps. First, a formula to be tested for unsatisfiability is translated into a normal form. Secondly, a family of resolution rules are used, to deal with the interactions between the various operators of the logics. In addition to a description of the normal form and the proof methods, we present some short worked examples and proposals for future work.
Work partially supported under EPSRC Research Grant GR/K57282.
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Fisher, M., Wooldridge, M., Dixon, C. (1996). A resolution-based proof method for temporal logics of knowledge and belief. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_72
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DOI: https://doi.org/10.1007/3-540-61313-7_72
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