107 research outputs found

    The Complexity of Reasoning for Fragments of Autoepistemic Logic

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    Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic

    Logical Omnipotence and Two notions of Implicit Belief

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    The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, which highlights the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence

    Extended RDF: Computability and Complexity Issues

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    ERDF stable model semantics is a recently proposed semantics for ERDF ontologies and a faithful extension of RDFS semantics on RDF graphs. In this paper, we elaborate on the computability and complexity issues of the ERDF stable model semantics. Based on the undecidability result of ERDF stable model semantics, decidability under this semantics cannot be achieved, unless ERDF ontologies of restricted syntax are considered. Therefore, we propose a slightly modified semantics for ERDF ontologies, called ERDF #n- stable model semantics. We show that entailment under this semantics is, in general, decidable and also extends RDFS entailment. Equivalence statements between the two semantics are provided. Additionally, we provide algorithms that compute the ERDF #n-stable models of syntax-restricted and general ERDF ontologies. Further, we provide complexity results for the ERDF #nstable model semantics on syntax-restricted and general ERDF ontologies. Finally, we provide complexity results for the ERDF stable model semantics on syntax-restricted ERDF ontologies

    Informatinio mąstymo ugdymo konstrukcionistinėje aplinkoje projektavimo moksliniai tyrimai: pragmatistinė perspektyva

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    [full article, abstract in English; abstract in Lithuanian] The article examines the modern computer-based educational environment and the requirements of the possible cognitive interface that enables the learner’s cognitive grounding by incorporating abductive reasoning into the educational process. Although the main emphasis is on cognitive and physiological aspects, the practical tools for enabling computational thinking in a modern constructionist educational environment are discussed. The presented analytical material and developed solutions are aimed at education with computers. However, the proposed solutions can be generalized in order to create a computer-free educational environment. The generalized paradigm here is pragmatism, considered as a philosophical assumption. By designing and creating a pragmatist educational environment, a common way of organizing computational thinking that enables constructionist educational solutions can be found.[straipsnis ir santrauka anglų kalba, santrauka lietuvių kalba] Straipsnyje nagrinėjama šiuolaikinė kompiuterinėmis technologijomis grįsta edukacinė aplinka. Aptariami kognityvinės sąsajos, skirtos besimokančiojo įgyjamoms žinioms sieti su realaus pasaulio objektais ar reiškiniais, reikalavimai. Šį susiejimą siūloma realizuoti į ugdymo procesą įtraukiant abdukcinius samprotavimus. Straipsnyje aptariamos praktinės priemonės informatiniam mąstymui ugdyti šiuolaikinėje konstrukcionistinėje aplinkoje, akcentuojant kognityvinius ir fiziologinius aspektus ir jungiant kelių paradigmų teorijas. Pateikta analitinė medžiaga ir siūlomi sprendimai skirti kompiuterinei ugdymo aplinkai, tačiau gali būti apibendrinti ir bendrajai ugdymo aplinkai be technologijų. Filosofine prielaida čia laikoma generalizuota pragmatizmo paradigma. Projektuojant ir kuriant pragmatistinę ugdymo aplinką, randamas informatinio mąstymo ugdymo naudojant konstrukcionistinius edukacinius sprendimus būdas

    The Complexity of Reasoning for Fragments of Default Logic

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    Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

    Commonsense axiomatizations for logic programs

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    AbstractVarious semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom
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