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Title Bridging the Gap between Classical Logic Based Formalisms and Logic Programs
Publication Date
Degree PhD
Discipline/Department Computer Science
Degree Level doctoral
University/Publisher Arizona State University
Abstract Different logic-based knowledge representation formalisms have different limitations either with respect to expressivity or with respect to computational efficiency. First-order logic, which is the basis of Description Logics (DLs), is not suitable for defeasible reasoning due to its monotonic nature. The nonmonotonic formalisms that extend first-order logic, such as circumscription and default logic, are expressive but lack efficient implementations. The nonmonotonic formalisms that are based on the declarative logic programming approach, such as Answer Set Programming (ASP), have efficient implementations but are not expressive enough for representing and reasoning with open domains. This dissertation uses the first-order stable model semantics, which extends both first-order logic and ASP, to relate circumscription to ASP, and to integrate DLs and ASP, thereby partially overcoming the limitations of the formalisms. By exploiting the relationship between circumscription and ASP, well-known action formalisms, such as the situation calculus, the event calculus, and Temporal Action Logics, are reformulated in ASP. The advantages of these reformulations are shown with respect to the generality of the reasoning tasks that can be handled and with respect to the computational efficiency. The integration of DLs and ASP presented in this dissertation provides a framework for integrating rules and ontologies for the semantic web. This framework enables us to perform nonmonotonic reasoning with DL knowledge bases. Observing the need to integrate action theories and ontologies, the above results are used to reformulate the problem of integrating action theories and ontologies as a problem of integrating rules and ontologies, thus enabling us to use the computational tools developed in the context of the latter for the former.
Subjects/Keywords Computer science; Artificial Intelligence; Knowledge Representation and Reasoning; Logic Programming; Nonmonotonic Reasoning; Reasoning about Actions; Rules and Ontologies
Country of Publication us
Record ID oai:arizonastate:14557
Repository asu
Date Retrieved
Date Indexed 2019-07-08
Grantor Arizona State University

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…light of further information). In order to overcome this limitation of first-order logic, there has been extensive research on nonmonotonic reasoning, and many formalisms have been proposed. Circumscription (McCarthy, 1980, 1986) and…

…Default Logic (Reiter, 1980) are among the first and most well-known nonmonotonic formalisms to have been introduced. These languages extend first-order logic and have been shown to be suitable for representing various commonsense reasoning…

…x29;. However, circumscription and default logic are hard to compute and thus lack efficient implementations. Nonmonotonic reasoning is also studied in the context of logic programs, and a number of declarative languages have been proposed. One of the…

Logic Knowledge Bases and Answer Set Programming Rules . . . . . . . . . . . . . . . . . . . . . 164 10.2 Relation to DL + log . . . . . . . . . . . . . . . . . . . . . . . 166 Discarding Datalog Safety . . . . . . . . . . . . . . . . . . . 169 10.3…

…Relation to Quantified Equilibrium Logic with Hybrid Rules . . 172 Review of Quantified Equilibrium Logic . . . . . . . . . . . . 172 Relation to the Quantified Equilibrium Logic Based Approach 173 10.4 Relation to g -hybrid Knowledge Bases…

…174 10.5 Relating to Nonmonotonic dl-programs . . . . . . . . . . . . . 175 Review of Nonmonotonic dl-programs . . . . . . . . . . . . 175 Relation to Nonmonotonic dl-programs . . . . . . . . . . . . 177 10.6 Strong Equivalence of Hybrid Knowledge…

…knowledge. A lot of work in the area is based on formal logic, and many logic-based formalisms have been proposed. However, developing a formalism that is both adequately expressive and efficiently computable has remained a constant fundamental challenge…

…First-order logic is widely used in KR&R. It forms the basis of many well-known knowledge representation languages. For example, Description Logics (DLs), which are widely studied in the context of the semantic web, are decidable fragments of…