Logic Programs with Ordered Disjunction (LPOD) is an extension of standard answer set programs to handle preference using the high-level construct of ordered disjunction whereas asprin is a recently proposed, general, flexible, and extensible framework that provides low-level constructs for representing preference in answer set programming. We present an encoding of LPOD in the language of asprin and the implementation LPOD2ASPRIN based on the encoding. Unlike the known method that applies only to a fragment of LPOD via the translation to Answer Set Optimization (ASO), our translation is general, direct, and simpler. It also leads to more efficient computation of LPOD using asprin.
more »
« less
Translating LPOD and CR-Prolog 2 into standard answer set programs
Abstract Logic Programs with Ordered Disjunction (LPOD) is an extension of standard answer set programs to handle preference using the construct of ordered disjunction, and CR-Prolog 2 is an extension of standard answer set programs with consistency restoring rules and LPOD-like ordered disjunction. We present reductions of each of these languages into the standard ASP language, which gives us an alternative way to understand the extensions in terms of the standard ASP language.
more »
« less
- Award ID(s):
- 1815337
- NSF-PAR ID:
- 10105987
- Date Published:
- Journal Name:
- Theory and Practice of Logic Programming
- Volume:
- 18
- Issue:
- 3-4
- ISSN:
- 1471-0684
- Page Range / eLocation ID:
- 589 to 606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling problems beyond NP with ASP is known to be complicated, on the one hand, and limited to problems in $\[\Sigma _2^P\]$ on the other. Inspired by the way Quantified Boolean Formulas extend SAT formulas to model problems beyond NP, we propose an extension of ASP that introduces quantifiers over stable models of programs. We name the new language ASP with Quantifiers (ASP(Q)). In the paper we identify computational properties of ASP(Q); we highlight its modeling capabilities by reporting natural encodings of several complex problems with applications in artificial intelligence and number theory; and we compare ASP(Q) with related languages. Arguably, ASP(Q) allows one to model problems in the Polynomial Hierarchy in a direct way, providing an elegant expansion of ASP beyond the class NP.more » « less
-
Abstract We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.more » « less
-
Abstract We present a probabilistic extension of action language ${\cal BC}$+$ . Just like ${\cal BC}$+$ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call p ${\cal BC}$+$ , is defined as a high-level notation of LP MLN programs—a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled in p ${\cal BC}$+$ and computed using an implementation of LP MLN .more » « less
-
more » « less
We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can make use of ASP rules to train a neural network better so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S1471068418000315
