Its apparent simplicity allows one to design very efficient and compact algorithms to tackle, in practice, problems lying at the first levels of the complexity classes. In this chapter, we first present the kind of A.I. problems that can typically be addressed by this formalism. Then, we ...
For first-order default logic these problems are not even semi-decidable [Reiter 1980]. This holds also for first-order autoepistemic logic even when quantifying into the scope of the modal operator is not allowed [Niemelä 1990]. If quantifying-in is allowed, the problems are highly undecid...
Another problem of interest in practice is the Longest Extension of Implicant problem [147] for DNF formulae. By analogy, we also consider the Longest Extension of Implicate problem for CNF formulae. Definition 26 Longest Extension of Implicant; FLEIt Let t be an implicant of F∈D, i.e. ...
Soh et al., 2017] T. Soh, M. Banbara, N. Tamura, and D. Le Berre. Solving Multiobjective Discrete Optimization Problems with Propositional Minimal Model Generation. In International Conference on Principles and Practice of Constraint Programming, pages 596-614. Springer, 2017....
[...]based on an assessment of State practice, the present report, even though there was available practice, was largely deductive, reflecting extrapolations of logic and offering broadpropositions,notexactly precise in terms of drafting, for consideration. ...
this algorithm effective in practice. Our algorithm has been implemented in a tree automata software library, called CETA [14], that can check the emptiness of propositional tree automata modulo associativity, commutativity, and identity.
firstorderlogic.Aftermanyyearsofdevelopment,deduc- tionsystemsfortheselogicsarenowincreasinglybeingap- pliedinpractice.Theoremproversforfirst-orderlogicare e.g.beingusedfortheverificationofcommunicationproto- cols(Weidenbach1999;G¨urdens&Peralta2000),hard-and ...
2003. Local-search tech- niques for propositional logic extended with cardinality con- straints. In Proc. of CP, 495-509.Liu, L., Truszczyński, M.: Local-search techniques for propositional logic extended with cardinality constraints. In: Principles and Practice of Constraint Programming-CP ...
One of the central problems of propositional logic is to find useful methods for recognizing tautologies; since A is a tautology if and only if ¬A is not satisfiable, this is essentially the same as the problem of finding methods for recognizing satisfiable formulas. Of course, the set of...
Abstract The aim of propositional algorithmic logic PAL is to investigate properties of program connectives and to develop tools useful in the practice of proving properties of program schemes. The tautologies of PAL become tautologies of algorithmic logic after replacing program variables by programs and...