We introduce formal proof systems based on tableau methods for analyzing computations in answer set programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategie...
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We introduce formal proof systems based on tableau methods for analyzing computations in answer set programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.
We describe an approach to modeling biological networks by action languages via answer set programming. To this end, we propose an action language for modeling biological networks, building on previous work by Baral e...
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We describe an approach to modeling biological networks by action languages via answer set programming. To this end, we propose an action language for modeling biological networks, building on previous work by Baral et al. We introduce its syntax and semantics along with a translation into answer set programming, an efficient Boolean Constraint programming Paradigm. Finally, we describe one of its applications, namely, the sulfur starvation response-pathway of the model plant Arabidopsis thaliana and sketch the functionality of our system and its usage.
The paper discusses some properties of system descriptions in action language– a recent extension of action language(also known as) bydefined fluents. We give a sufficient condition guaranteeing that states of ansyst...
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The paper discusses some properties of system descriptions in action language– a recent extension of action language(also known as) bydefined fluents. We give a sufficient condition guaranteeing that states of ansystem description are fully determined by statics and inertial fluents. In system descriptions satisfying this condition, defined fluents simply facilitate the description of dynamic domains; they are not essential and can be eliminated. We use our sufficient condition to identify a common core of action languagesand. This is an expansion of the work of , who identified a common core of languagesand. The results presented in this paper are based on the close relationship between action languages and the theory of logic programs under the answerset semantics.
answer set programming (ASP) is a logic programming based, truly declarative formalism for general purpose problem solving. Its declarative nature allows users to solve problems by defining what the solutions are inst...
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answer set programming (ASP) is a logic programming based, truly declarative formalism for general purpose problem solving. Its declarative nature allows users to solve problems by defining what the solutions are instead of how to find them. Complete lack of an imperative component in ASP makes creation of end user applications or integration with other systems demanding. External tools that can process and interpret the output of ASP solvers are needed. To address this issue in the case of simple applications with an input - output interaction loop we introduce a framework for iterative logic applications. Such applications consist of a core logic program that is used to evaluate user actions w.r.t. their current state and to derive a new state of the application. We take care to define the framework in a way that allows it to be used also with other formalism, especially SAT solvers. We also present a web based implementation of such framework for ASP.
We propose a combination of logic programming under the answerset semantics with the description logics SHIF(D) and SHOIN(D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, w...
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We propose a combination of logic programming under the answerset semantics with the description logics SHIF(D) and SHOIN(D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or di-programs), which consist of a description logic knowledge base L and a finite set P of description logic rules (or dl-rules). Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies. They allow for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We define a suite of semantics for various classes of dl-programs, which conservatively extend the standard semantics of the respective classes and coincide with it in absence of a description logic knowledge base. More concretely, we generalize positive, stratified, and arbitrary normal logic programs to dl-programs, and define a Herbrand model semantics for them. We show that they have similar properties as ordinary logic programs, and also provide fixpoint characterizations in terms of (iterated) consequence operators. For arbitrary dl-programs, we define answersets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answerset semantics, which are based on reductions to the semantics of positive dl-programs and ordinary positive logic programs, respectively. We also show how the weak answersets can be computed utilizing answersets of ordinary normal logic programs. Furthermore, we show how some advanced reasoning tasks for the Semantic Web, including different forms of closed-world reasoning and default reasoning, as well as DL-safe rules, can be realized on top of dl-programs. Finally, we give a precise picture of the computational complexity of dl-programs, and we describe efficient algorithms and a prototype implementation of dl-programs which is available on
This article studies a semantics of multiple logic programs, and synthesizes a program having such a collective semantics. More precisely, the following two problems are considered: given two logic programs P-1 and P-...
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This article studies a semantics of multiple logic programs, and synthesizes a program having such a collective semantics. More precisely, the following two problems are considered: given two logic programs P-1 and P-2, which have the collections of answersets AS(P-1) and AS(P-2), respectively;(i) find a program Q which has the set of answersets such that AS(Q) = AS(P-1). AS(P2);(ii) find a program R which has the set of answersets such that AS(R) = AS(P1) boolean AND AS(P2). A program Q satisfying the condition (i) is called generous coordination of P-1 and P-2;and R satisfying (ii) is called rigorous coordination of P-1 and P-2. Generous coordination retains all of the answersets of each program, but permits the introduction of additional answersets of the other program. By contrast, rigorous coordination forces each program to give up some answersets, but the result remains within the original answersets for each program. Coordination provides a program that reflects the meaning of two or more programs. We provide methods for constructing these two types of coordination and address its application to logic-based multi-agent systems.
This paper contains a survey of the main definitions and results obtained to date related to Temporal Equilibrium Logic, a nonmonotonic hybrid approach that combines Equilibrium Logic (the best-known logical character...
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This paper contains a survey of the main definitions and results obtained to date related to Temporal Equilibrium Logic, a nonmonotonic hybrid approach that combines Equilibrium Logic (the best-known logical characterisation for the stable models semantics of logic programs) with Linear-Time Temporal Logic.
We introduce a knowledge representation language AC(C) extending the syntax and semantics of ASP and CR-Prolog, give some examples of its use, and present an algorithm, ACsolver, for computing answersets of AC(C) pro...
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We introduce a knowledge representation language AC(C) extending the syntax and semantics of ASP and CR-Prolog, give some examples of its use, and present an algorithm, ACsolver, for computing answersets of AC(C) programs. The algorithm does not require full grounding of a program and combines "classical" ASP solving methods with constraint logic programming techniques and CR-Prolog based abduction. The AC(C) based approach often allows to solve problems which are impossible to solve by more traditional ASP solving techniques. We believe that further investigation of the language and development of more efficient and reliable solvers for its programs can help to substantially expand the domain of applicability of the answer set programming paradigm.
Defence trees are used to represent attack and defence strategies in security scenarios;the aim in such scenarios is to select the best set of countermeasures that are able to stop all the vulnerabilities. In order to...
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Defence trees are used to represent attack and defence strategies in security scenarios;the aim in such scenarios is to select the best set of countermeasures that are able to stop all the vulnerabilities. In order to represent preferences among possible countermeasures of a given attack, defence trees are enriched with conditional preferences, obtaining a new structure called CP-defence tree. In this paper we transform a CP-defence tree with preferences among attacks and countermeasures in an answerset Optimization (ASO) program. The ASO program, representing the overall scenario, is a special composition of the programs associated to each branch of a CP-defence tree. We describe an implementation that select the best set of countermeasure able to mitigate all the vulnerabilities by computing the optimal answerset of the corresponding ASO program.
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