Reasoning about Minimal Belief and Negation as Failure

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic

Dynamic epistemic modelling

This paper introduces DEMO, a Dynamic Epistemic Modelling tool. DEMO llows modelling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, translation of dynamic epistemic formulas to PDL formulas, and so on. The paper implements a reduction of dynamic epistemic logic to PDL. The reduction of dynamic epistemic logic to automata PDL from Van Benthem and Kooi is also discussed and implemented. Epistemic models are minimized under bisimulation, and update action models are minimized under action emulation (the appropriate structural notion for having the same update effect). The paper is an exemplar of tool building for epistemic updatelogic. It contains the full code of an implementation in Haskell in `literate programming' style, of DEM