In this paper, we propose a variant of answer set programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, ...
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In this paper, we propose a variant of answer set programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the syntax of First Order Logic with equality and the semantics of Quantified Equilibrium Logic with evaluable functions (QEL(F)(=)). Then, we proceed to incorporate a new kind of logical term, intensional set (a construct commonly used to denote the set of objects characterised by a given formula), and to extend QEL(F)(=) semantics for this new type of expression. In our extended approach, intensional sets can be arbitrarily used as predicate or function arguments or even nested inside other intensional sets, just as regular first-order logical terms. As a result, aggregates can be naturally formed by the application of some evaluable function (count, sum, maximum, etc) to a set of objects expressed as an intensional set. This approach has several advantages. First, while other semantics for aggregates depend on some syntactic transformation (either via a reduct or a formula translation), the QEL(F)(=) interpretation treats them as regular evaluable functions, providing a compositional semantics and avoiding any kind of syntactic restriction. Second, aggregates can be explicitly defined now within the logical language by the simple addition of formulas that fix their meaning in terms of multiple applications of some (commutative and associative) binary operation. For instance, we can use recursive rules to define sum in terms of integer addition. Last, but not least, we prove that the semantics we obtain for aggregates coincides with the one defined by Gelfond and Zhang for the Alog language, when we restrict to that syntactic fragment.
Enterprise/Corporate ontologies are widely adopted to conceptualize business enterprise information. In this area, the semantic peculiarities of answer set programming (ASP), like the Closed World Assumption (CWA) and...
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Enterprise/Corporate ontologies are widely adopted to conceptualize business enterprise information. In this area, the semantic peculiarities of answer set programming (ASP), like the Closed World Assumption (CWA) and the Unique Name Assumption (UNA), are more appropriate than the OntologyWeb Language (OWL) assumptions, also because such ontologies frequently stem from relational databases, where both CWA and UNA are adopted. This article presents OntoDLV, a system based on ASP for the specification and reasoning on enterprise ontologies. OntoDLV implements a powerful ontology representation language, called OntoDLP, extending (disjunctive) ASP with all the main ontology features including classes, inheritance, relations and axioms. OntoDLP is strongly typed, and includes also complex type constructors, like lists and sets. Importantly, OntoDLV supports a powerful interoperability mechanism with OWL, allowing the user to retrieve information from OWL ontologies, and build rule-based reasoning on top of OWL ontologies. The system is already used in a number of real-world applications including agent-based systems, information extraction, and text classification.
One of the major reasons for the success of answer set programming in recent years was the shift from a theorem proving to a constraint programming view: problems are represented such that stable models, respectively ...
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One of the major reasons for the success of answer set programming in recent years was the shift from a theorem proving to a constraint programming view: problems are represented such that stable models, respectively answersets, rather than theorems correspond to solutions. This shift in perspective proved extremely fruitful in many areas. We believe that going one step further from a "hard'' to a "soft'' constraint programming paradigm, or, in other words, to a paradigm of qualitative optimization, will prove equally fruitful. In this paper we try to support this claim by showing that several generic problems in logic based problem solving can be understood as qualitative optimization problems, and that these problems have simple and elegant formulations given adequate optimization constructs in the knowledge representation language.
Intelligent tutors that emulate one-on-one tutoring with a human have been shown to effectively support student learning, but these systems are often challenging to build. Most methods for implementing tutors focus on...
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ISBN:
(纸本)9783030232047;9783030232030
Intelligent tutors that emulate one-on-one tutoring with a human have been shown to effectively support student learning, but these systems are often challenging to build. Most methods for implementing tutors focus on generating intelligent explanations, rather than generating practice problems and problem progressions. In this work, we explore the possibility of using a single model of a learning domain to support the generation of both practice problems and intelligent explanations. In the domain of algebra, we show how problem generation can be supported by modeling if-then production rules in the logic programming language answer set programming. We also show how this model can be authored such that explanations can be generated directly from the rules, facilitating both worked examples and real-time feedback during independent problem-solving. We evaluate this approach through a proof-of-concept implementation and two formative user studies, showing that our generated content is of appropriate quality. We believe this approach to modeling learning domains has many exciting advantages.
We study the problem of finding optimal plans for multiple teams of robots through a mediator, where each team is given a task to complete in its workspace on its own and where teams are allowed to transfer robots bet...
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We study the problem of finding optimal plans for multiple teams of robots through a mediator, where each team is given a task to complete in its workspace on its own and where teams are allowed to transfer robots between each other, subject to the following constraints: 1) teams (and the mediator) do not know about each other's workspace or tasks (e.g., for privacy purposes);2) every team can lend or borrow robots, but not both (e.g., transportation/calibration of robots between/for different workspaces is usually costly). We present a mathematical definition of this problem and analyze its computational complexity. We introduce a novel, logic-based method to solve this problem, utilizing action languages and answer set programming for representation, and the state-of-the-art ASP solvers for reasoning. We show the applicability and usefulness of our approach by experiments on various scenarios of responsive and energy-efficient cognitive factories.
We argue that turning a logic program into a set of completed definitions can be sometimes thought of as the "reverse engineering" process of generating a set of conditions that could serve as a specificatio...
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We argue that turning a logic program into a set of completed definitions can be sometimes thought of as the "reverse engineering" process of generating a set of conditions that could serve as a specification for it. Accordingly, it may be useful to define completion for a large class of answer set programming (ASP) programs and to automate the process of generating and simplifying completion formulas. Examining the output produced by this kind of software may help programmers to see more clearly what their program does, and to what degree its behavior conforms with their expectations. As a step toward this goal, we propose here a definition of program completion for a large class of programs in the input language of the ASP grounder gringo, and study its properties.
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonoto...
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Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non -deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non -deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.
In this paper, the class of possibilistic nested logic programs is introduced. These possibilistic logic programs allow us to use nested expressions in the bodies and heads of their rules. By considering a possibilist...
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In this paper, the class of possibilistic nested logic programs is introduced. These possibilistic logic programs allow us to use nested expressions in the bodies and heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answersets for nested logic programs and the proof theory of possibilistic logic is defined. In order to define a general method for computing the possibilistic answersets of a possibilistic nested program, the idea of equivalence between possibilistic nested programs is explored. By considering properties of equivalence between possibilistic programs, a process of transforming a possibilistic nested logic program into a possibilistic disjunctive logic program is defined. Given that our approach is an extension of answer set programming, we also explore the concept of strong equivalence between possibilistic nested logic programs. To this end, we introduce the concept of poss SE-models. Therefore, we show that two possibilistic nested logic programs are strong equivalents whenever they have the same poss SE-models. The expressiveness of the possibilistic nested logic programs is illustrated by a scenario from the medical domain. In particular, we exemplify how possibilistic nested logic programs are expressive enough for capturing medical guidelines which are pervaded by vagueness and qualitative information. (C) 2015 Elsevier Inc. All rights reserved.
LPMLN is a recent addition to probabilistic logic programming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov Logic ...
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LPMLN is a recent addition to probabilistic logic programming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov Logic is defined. We present two implementations of LPMLN, LPMLN2ASP and LPMLN2MLN. System LPMLN2ASP translates LPMLN programs into the input language of answerset solver CLINGO, and using weak constraints and stable model enumeration, it can compute most probable stable models as well as exact conditional and marginal probabilities. System LPMLN2MLN translates LPMLN programs into the input language of Markov Logic solvers, such as alchemy, TUFFY, and ROCKIT, and allows for performing approximate probabilistic inference on LPMLN programs. We also demonstrate the usefulness of the LPMLN systems for computing other languages, such as ProbLog and Pearl's Causal Models, that are shown to be translatable into LPMLN.
Generalising and re-using knowledge learned while solving one problem instance has been neglected by state-of-the-art answerset solvers. We suggest a new approach that generalises learned nogoods for re-use to speed-...
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Generalising and re-using knowledge learned while solving one problem instance has been neglected by state-of-the-art answerset solvers. We suggest a new approach that generalises learned nogoods for re-use to speed-up the solving of future problem instances. Our solution combines well-known ASP solving techniques with deductive logic-based machine learning. Solving performance can be improved by adding learned non-ground constraints to the original program. We demonstrate the effects of our method by means of realistic examples, showing that our approach requires low computational cost to learn constraints that yield significant performance benefits in our test cases. These benefits can be seen with ground-and-solve systems as well as lazy-grounding systems. However, ground-and-solve systems suffer from additional grounding overheads, induced by the additional constraints in some cases. By means of conflict minimization, non-minimal learned constraints can be reduced. This can result in significant reductions of grounding and solving efforts, as our experiments show.
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