scholarly journals Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

2021 ◽  
Vol 21 (5) ◽  
pp. 575-592
Author(s):  
VIKTOR BESIN ◽  
MARKUS HECHER ◽  
STEFAN WOLTRAN
Keyword(s):  
Epistemic Logic ◽  
Complexity Analysis ◽  
Quantitative Reasoning ◽  
Decision Problems ◽  
Logic Programs ◽  
Counting Problems ◽  
World Views ◽  
Modal Operators ◽  
Programming Paradigm ◽  
Answer Sets

AbstractExtending the popular answer set programming paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, that is, contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently.

Answer Sets and the Language of Answer Set Programming

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 7-12 ◽  
Author(s):  
Vladimir Lifschitz
Keyword(s):  
Answer Set Programming ◽  
Declarative Programming ◽  
Logic Programs ◽  
Special Issue ◽  
Programming Paradigm ◽  
Introductory Article ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Semantics Of Logic Programs ◽  
Answer Set

Answer set programming is a declarative programming paradigm based on the answer set semantics of logic programs. This introductory article provides the mathematical background for the discussion of answer set programming in other contributions to this special issue.

scholarly journals eclingo : A Solver for Epistemic Logic Programs

2020 ◽  
Vol 20 (6) ◽  
pp. 834-847
Author(s):  
Pedro Cabalar ◽  
Jorge Fandinno ◽  
Javier Garea ◽  
Javier Romero ◽  
Torsten Schaub
Keyword(s):  
Epistemic Logic ◽  
State Of The Art ◽  
Answer Set Programming ◽  
Search Space ◽  
Second Step ◽  
Programming System ◽  
Logic Programs ◽  
Input Language ◽  
Truth Values ◽  
Answer Sets

AbstractWe 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.

scholarly journals About Epistemic Negation and World Views in Epistemic Logic Programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 790-807 ◽  
Author(s):  
STEFANIA COSTANTINI
Keyword(s):  
Epistemic Logic ◽  
Answer Set Programming ◽  
Logic Programs ◽  
World Views ◽  
Recent Approach ◽  
Answer Set

AbstractIn this paper we consider Epistemic Logic Programs, which extend Answer Set Programming (ASP) with “ epistemic operators” and “ epistemic negation”, and a recent approach to the semantics of such programs in terms ofWorld Views. We propose some observations on the existence and number of world views. We show how to exploit an extended ASP semantics in order to: (i) provide a characterization of world views, different from existing ones; (ii) query world views and query the whole set of world views.

scholarly journals On Computing World Views of Epistemic Logic Programs

2017 ◽  
Author(s):  
Tran Cao Son ◽  
Tiep Le ◽  
Patrick Kahl ◽  
Anthony Leclerc
Keyword(s):  
Epistemic Logic ◽  
Experimental Analysis ◽  
World View ◽  
Search Space ◽  
Planning System ◽  
Logic Programs ◽  
World Views ◽  
Future Work ◽  
Novel Algorithm ◽  
Answer Set

This paper presents a novel algorithm for computing world views of different semantics of epistemic logic programs (ELP) and two of its realization, called Ep-asp (for an older semantics) and Ep-asp^{se} (for the newest semantics), whose implementation builds on the theoretical advancement in the study of ELPs and takes advantage of the multi-shot computation paradigm of the answer set solver Clingo. The new algorithm differs from the majority of earlier algorithms in its strategy. Specifically, it computes one world view at a time and utilizes properties of world views to reduce its search space. It starts by computing an answer set and then determines whether or not a world view containing this answer set exists. In addition, it allows for the computation to focus on world views satisfying certain properties. The paper includes an experimental analysis of the performance of the two solvers comparing against a recently developed solver. It also contains an analysis of their performance in goal directed computing against a logic programming based conformant planning system, dlv-k. It concludes with some final remarks and discussion on the future work.

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

scholarly journals onlineSPARC: A Programming Environment for Answer Set Programming

2018 ◽  
Vol 19 (2) ◽  
pp. 262-289 ◽  
Author(s):  
ELIAS MARCOPOULOS ◽  
YUANLIN ZHANG
Keyword(s):  
High School Students ◽  
Logic Programming ◽  
Answer Set Programming ◽  
Programming Environment ◽  
Logic Programs ◽  
School Students ◽  
Major Barrier ◽  
Simple Interface ◽  
Answer Sets ◽  
Answer Set

AbstractRecent progress in logic programming (e.g. the development of the answer set programming (ASP) paradigm) has made it possible to teach it to general undergraduate and even middle/high school students. Given the limited exposure of these students to computer science, the complexity of downloading, installing, and using tools for writing logic programs could be a major barrier for logic programming to reach a much wider audience. We developed onlineSPARC, an online ASP environment with a self-contained file system and a simple interface. It allows users to type/edit logic programs and perform several tasks over programs, including asking a query to a program, getting the answer sets of a program, and producing a drawing/animation based on the answer sets of a program.

scholarly journals Vicious Circle Principle and Logic Programs with Aggregates

2014 ◽  
Vol 14 (4-5) ◽  
pp. 587-601 ◽  
Author(s):  
MICHAEL GELFOND ◽  
YUANLIN ZHANG
Keyword(s):  
Knowledge Representation ◽  
Vicious Circle ◽  
Logic Programs ◽  
Vicious Circle Principle ◽  
Knowledge Representation Language ◽  
Representation Language ◽  
Answer Sets ◽  
Mathematical Semantics

AbstractThe paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.

scholarly journals Beyond NP: Quantifying over Answer Sets

2019 ◽  
Vol 19 (5-6) ◽  
pp. 705-721
Author(s):  
GIOVANNI AMENDOLA ◽  
FRANCESCO RICCA ◽  
MIROSLAW TRUSZCZYNSKI
Keyword(s):  
Answer Set Programming ◽  
The Other ◽  
Polynomial Hierarchy ◽  
Programming Paradigm ◽  
Quantified Boolean Formulas ◽  
Boolean Formulas ◽  
The One ◽  
Image Position ◽  
Answer Sets ◽  
Computational Properties

AbstractAnswer 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.

scholarly journals Polytool: Polynomial interpretations as a basis for termination analysis of logic programs

2010 ◽  
Vol 11 (1) ◽  
pp. 33-63 ◽  
Author(s):  
MANH THANG NGUYEN ◽  
DANNY DE SCHREYE ◽  
JÜRGEN GIESL ◽  
PETER SCHNEIDER-KAMP
Keyword(s):  
Logic Programs ◽  
Termination Analysis ◽  
Rewrite Systems ◽  
Analysis Techniques ◽  
Programming Paradigm ◽  
Generating Polynomial ◽  
Direct Generalization ◽  
Term Rewrite Systems

AbstractOur goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations—very well known in the context of term rewrite systems—to obtain new (nontransformational) termination analysis techniques for definite logic programs (LPs). This leads to an approach that can be seen as a direct generalization of the traditional techniques in termination analysis of LPs, where linear norms and level mappings are used. Our extension generalizes these to arbitrary polynomials. We extend a number of standard concepts and results on termination analysis to the context of polynomial interpretations. We also propose a constraint-based approach for automatically generating polynomial interpretations that satisfy the termination conditions. Based on this approach, we implemented a new tool, called Polytool, for automatic termination analysis of LPs.

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