The universe of propositional approximations
Theoretical Computer Science - Logic, language, information and computation
Approximations of Modal Logic K
Electronic Notes in Theoretical Computer Science (ENTCS)
Prime implicates for approximate reasoning
KSEM'07 Proceedings of the 2nd international conference on Knowledge science, engineering and management
Semantics and proof-theory of depth bounded Boolean logics
Theoretical Computer Science
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Real agents (natural or artificial) are limited in their reasoning capabilities. In this paper, we present a general framework for modelling limited reasoning based on approximate reasoning and discuss its properties. We start from Cadoli and Schaerf's approximate entailment. We first extend their system to deal with the full language of propositional logic. A tableau inference system is proposed for the extended system together with a subclassical semantics; it is shown that this new approximate reasoning system is sound and complete with respect to this semantics. We show how this system can be incrementally used to move from one approximation to the next until the reasoning limitation is reached. We also present a sound and complete axiomatization of the extended system. We note that although the extension is more expressive than the original system, it offers less control over the approximation process. We then propose a more general system and show that it keeps the increased expressivity and recovers the control. A sound and complete formulation for this new system is given and its expressivity and control advantages are formally proved.