The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative gene...
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The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative generation of ground programs thus achieving a significant payoff in terms of computing time. However, this may require some additional amount of memory and/or the manual addition of operational directives in the declarative knowledge base at hand. We introduce a new strategy for generating series of monotonically growing propositional programs. The proposedovergrounded programs with tailoring(OPTs) can be updated and reused in combination with consecutive inputs. With respect to earlier approaches, ourtailored simplificationtechnique reduces the size of instantiated programs. A maintained OPT slowly grows in size from an iteration to another while the update cost decreases, especially in later iterations. In this paper we formally introduce tailored embeddings, a family of equivalence-preserving ground programs which are at the theoretical basis of OPTs and we describe their properties. We then illustrate an OPT update algorithm and report about our implementation and its performance.
Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the G...
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Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete, and preferred semantics.
Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set programming (ASP), a convenient tool for pr...
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We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set programming system clingo. The input language of eclingo uses the syntax extension capabilities of clin...
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We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set programming system clingo. The input language of eclingo uses the syntax extension capabilities of clingo to define subjective literals that, as usual in epistemic logic programs, allow for checking the truth of a regular literal in all or in some of the answer sets of a program. The eclingo solving process follows a guess and check strategy. It first generates potential truth values for subjective literals and, in a second step, it checks the obtained result with respect to the cautious and brave consequences of the program. This process is implemented using the multi-shot functionalities of clingo. We have also implemented some optimisations, aiming at reducing the search space and, therefore, increasing eclingo 's efficiency in some scenarios. Finally, we compare the efficiency of eclingo with two state-of-the-art solvers for epistemic logic programs on a pair of benchmark scenarios and show that eclingo generally outperforms their obtained results.
Answer-Set programming (ASP) is a powerful and expressive knowledge representation paradigm with a significant number of applications in logic-based AI. The traditional ground-and-solve approach, however, requires ASP...
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Answer-Set programming (ASP) is a powerful and expressive knowledge representation paradigm with a significant number of applications in logic-based AI. The traditional ground-and-solve approach, however, requires ASP programs to be grounded upfront and thus suffers from the so-called grounding bottleneck (i.e., ASP programs easily exhaust all available memory and thus become unsolvable). As a remedy, lazy-grounding ASP solvers have been developed, but many state-of-the-art techniques for grounded ASP solving have not been available to them yet. In this work we present, for the first time, adaptions to the lazy-grounding setting for many important techniques, like restarts, phase saving, domain-independent heuristics, and learned-clause deletion. Furthermore, we investigate their effects and in general observe a large improvement in solving capabilities and also uncover negative effects in certain cases, indicating the need for portfolio solving as known from other solvers.
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculiLKandLJenjoy cut elimination. The ...
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In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculiLKandLJenjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. In this paper, we use coinductive Horn clause theories to show that cut is not eliminable in a coinductive extension ofLJ, a system we callCLJ. We derive two further practical results from this study. We show that CoLP by Gupta et al. gives rise to cut-free proofs inCLJwith fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics for discovery of cut formulae inCLJ.
This paper formally compares some central notions from two well-known formalisms for rule-based argumentation,DeLPandASPIC(+). The comparisons especially focus on intuitive adequacy and inter-translatability, consiste...
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This paper formally compares some central notions from two well-known formalisms for rule-based argumentation,DeLPandASPIC(+). The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out thatDeLP's definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud's rationality postulates of strict closure and indirect consistency. For some special cases, theDeLPdefinitions are shown to fare better thanASPIC(+). Next, it is argued that there are reasons to consider a variant ofDeLPwith grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions onASPIC(+)arguments, a one-to-many correspondence betweenASPIC(+)arguments andDeLParguments is identified in such a way that if theDeLPwarranting procedure is changed to grounded semantics, then 'sDeLPnotion of warrant andASPIC(+)'s notion of justification are equivalent. This result is proven for three alternative definitions of attack.
Macroprogramming refers to the theory and practice of conveniently expressing the macro(scopic) behaviour of a system using a single program. Macroprogramming approaches are motivated by the need of effectively captur...
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Game logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in respo...
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ISBN:
(数字)9783030449148
ISBN:
(纸本)9783030449148;9783030449131
Game logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's actions. We thus develop Constructive Game logic, which extends Parikh's Game logic (GL) with constructivity and with first-order programs a la Pratt's first-order dynamic logic (DL). Our major contributions include: 1. a novel realizability semantics capturing the adversarial dynamics of games, 2. a natural deduction calculus and operational semantics describing the computational meaning of strategies via proof-terms, and 3. theoretical results including soundness of the proof calculus w.r.t. realizability semantics, progress and preservation of the operational semantics of proofs, and Existential Properties enabling the extraction of computational artifacts from game proofs. Together, these results provide the most general account of a Curry-Howard interpretation for any program logic to date, and the first at all for Game logic.
Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for vari...
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Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i)interval propagators completionthat allows abstract domains to exchange bound constraints, and (ii)delayed productwhich exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logicprogramming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose theshared productto combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem.
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