Decision Procedure for a Fragment of Mutual Belief Logic with Quantified Agent Variables
نویسندگان
چکیده
A deduction-based decision procedure for a fragment of mutual belief logic with quantified agent variables (MBQL) is presented. A language of MBQL contains variables and constants for agents. The language ofMBQL is convenient to describe properties of rational agents when the number of agents is not known in advance. The multi-modal logic KD45n extended with restricted occurrences of quantifiers for agent variables is a component ofMBQL. For this logic loop-check-free sequent calculus is proposed. This calculus corresponds to contraction-free calculus and does not require to translate sequents in a certain normal form. Another new point of presented decision procedure is existentially invertible separation rules. For a sequent containing occurrences of mutual belief modality two type of loop-check can be used: for positive occurrences of mutual belief modality loop-check can be used to find non-logical (loop-type) axioms, and for negative ones — to establish a non-derivability criterion.
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