An essay in combinatory dynamic logic
Information and Computation
Basic proof theory
Displaying modal logic
Specifying Message Passing and Time-Critical Systems with Temporal Logic
Specifying Message Passing and Time-Critical Systems with Temporal Logic
Prefixed tableaux systems for modal logics with enriched languages
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
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We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL≠) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus dMNTL for MNTL mimic those of the display calculus δMTL≠= for MTL≠=. Since δMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of δMNTL by addition of structural rules satisfying Belnap's conditions (C2)-(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of δMNTL also admit cut-free display calculi.