Probabilistic logicprogramming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in ...
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Probabilistic logicprogramming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was investigated as the strongest form of domain size dependence, in which query marginals are completely independent of the domain size. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to an acyclic probabilistic logic program consisting only of determinate clauses over probabilistic facts. We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for the projective families of distributions expressible by probabilistic logic programs.
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propo...
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In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.
When we want to compute the probability of a query from a probabilistic answer set program, some parts of a program may not influence the probability of a query, but they impact on the size of the grounding. Identifyi...
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When we want to compute the probability of a query from a probabilistic answer set program, some parts of a program may not influence the probability of a query, but they impact on the size of the grounding. Identifying and removing them is crucial to speed up the computation. Algorithms for SLG resolution offer the possibility of returning the residual program which can be used for computing answer sets for normal programs that do have a total well-founded model. The residual program does not contain the parts of the program that do not influence the probability. In this paper, we propose to exploit the residual program for performing inference. Empirical results on graph datasets show that the approach leads to significantly faster inference. The paper has been accepted at the ICLP2024 conference and under consideration in theory and practice of logic programming (TPLP).
Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to ...
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Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions;in particular the Godel and Lukasiewicz fuzzy connectives are usually considered, due to their properties. Although the Godel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. The paper analyzes a translation of FASP programs into satisfiability modulo theories (SMT), which in general produces quantified formulas because of the minimality of the semantics. Structural properties of many FASP programs allow to eliminate the quantification, or to sensibly reduce the number of quantified variables. Indeed, integrality constraints can replace recursive rules commonly used to force Boolean interpretations, and completion subformulas can guarantee minimality for acyclic programs with atomic heads. Moreover, head cycle free rules can be replaced by shifted subprograms, whose structure depends on the eliminated head connective, so that ordered completion may replace the minimality check if also Lukasiewicz disjunction in rule bodies is acyclic. The paper also presents and evaluates a prototype system implementing these translations.
In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e., the issue of how ontologies (and semantics conveyed by them) can help solvi...
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In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e., the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of Knowledge Representation (KR) aspects related to databases. In particular, we investigate this issue from the 1LP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as I LP problems and can benefit from the expressive and deductive power of the KR framework DL+LOG(V). We illustrate the application scenarios by means of examples.
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, that is, opera...
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Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, that is, operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola et al., and (3) we generalize the characterizations of disjunctive logic programs to disjunctive logic programs with aggregates.
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constrain...
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We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the generalization involves nondeterminism. Our main results demonstrate that our formalism is a common generalization of (1) normal logicprogramming with its semantics of models, supported models and stable models, (2) logicprogramming with weight atoms (Iparse programs) with the semantics of stable models, as defined by Niemela, Simons and Soininen, and (3) of disjunctive logicprogramming with the possible-model semantics of Sakama and Inoue.
(ECLPSe)-P-i is a Prolog-based programming system, aimed at the development and deployment of constraint programming applications. It is also used for teaching most aspects of combinatorial problem solving, for exampl...
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(ECLPSe)-P-i is a Prolog-based programming system, aimed at the development and deployment of constraint programming applications. It is also used for teaching most aspects of combinatorial problem solving, for example, problem modelling, constraint programming, mathematical programming and search techniques. It uses an extended Prolog as its high-level modelling and control language, complemented by several constraint solver libraries, interfaces to third-party solvers, an integrated development environment and interfaces for embedding into host environments. This paper discusses language extensions, implementation aspects, components, and tools that we consider relevant on the way from logicprogramming to Constraint logicprogramming.
Answer Set programming (ASP) is a prominent knowledge representation language with roots in logicprogramming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchm...
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Answer Set programming (ASP) is a prominent knowledge representation language with roots in logicprogramming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on logicprogramming and Non-Monotonic Reasoning (LPNMR 2017).
On the one hand, termination analysis of logic programs is now a fairly established research topic within the logicprogramming community. On the other hand, non-termination analysis seems to remain a much less attrac...
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On the one hand, termination analysis of logic programs is now a fairly established research topic within the logicprogramming community. On the other hand, non-termination analysis seems to remain a much less attractive Subject. If we divide this line of research into two kinds of approaches, dynamic versus static analysis, this paper belongs to the latter. It proposes a criterion for detecting non-terminating atomic queries with respect to binary constraint logicprogramming (CLP) rules, which strictly generalizes our previous works on this subject. We give a generic operational definition and an implemented logical form of this criterion. Then we show that the logical form is correct and complete with respect to the operational definition.
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