scholarly journals Answer Set Programming for Regular Inference

2020 ◽  
Vol 10 (21) ◽  
pp. 7700
Author(s):  
Wojciech Wieczorek ◽  
Tomasz Jastrzab ◽  
Olgierd Unold
Keyword(s):  
Finite Automaton ◽  
Logic Program ◽  
Answer Set Programming ◽  
Exact Algorithms ◽  
Deterministic Finite Automaton ◽  
Inductive Synthesis ◽  
Cpu Time ◽  
Series Of Experiments ◽  
Answer Set ◽  
Benchmark Sets

We propose an approach to non-deterministic finite automaton (NFA) inductive synthesis that is based on answer set programming (ASP) solvers. To that end, we explain how an NFA and its response to input samples can be encoded as rules in a logic program. We then ask an ASP solver to find an answer set for the program, which we use to extract the automaton of the required size. We conduct a series of experiments on some benchmark sets, using the implementation of our approach. The results show that our method outperforms, in terms of CPU time, a SAT approach and other exact algorithms on all benchmarks.

scholarly journals Grounding and Solving in Answer Set Programming

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 25-32 ◽  
Author(s):  
Benjamin Kaufmann ◽  
Nicola Leone ◽  
Simona Perri ◽  
Torsten Schaub
Keyword(s):  
Problem Solving ◽  
Propositional Logic ◽  
Logic Program ◽  
Answer Set Programming ◽  
Key Issues ◽  
Answer Sets ◽  
Answer Set

Answer set programming is a declarative problem solving paradigm that rests upon a workflow involving modeling, grounding, and solving. While the former is described by Gebser and Schaub (2016), we focus here on key issues in grounding, or how to systematically replace object variables by ground terms in a effective way, and solving, or how to compute the answer sets of a propositional logic program obtained by grounding.

A Roadmap on Updates

2009 ◽  
pp. 2261-2267
Author(s):  
Fernando Zacarías Flores ◽  
Dionicio Zacarías Flores ◽  
Rosalba Cuapa Canto ◽  
Luis Miguel Guzmán Muñoz
Keyword(s):  
Standard Model ◽  
Logic Programming ◽  
Structural Properties ◽  
Relational Databases ◽  
Logic Program ◽  
Answer Set Programming ◽  
Central Issue ◽  
The Standard Model ◽  
Answer Set

Updates, is a central issue in relational databases and knowledge databases. In the last years, it has been well studied in the non-monotonic reasoning paradigm. Several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997), (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). However, recently a set of proposals has been characterized to propose mechanisms of updates based on logic and logic programming. All these mechanisms are built on semantics based on structural properties (Eiter, Fink, Sabattini & Thompits, 2000) (Leite, 2002) (Banti, Alferes & Brogi, 2003) (Zacarias, 2005). Furthermore, all these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in(De Schreye, Hermenegildo, & Pereira, 1999).

scholarly journals Knowledge Forgetting in Answer Set Programming

2014 ◽  
Vol 50 ◽  
pp. 31-70 ◽  
Author(s):  
Y. Wang ◽  
Y. Zhang ◽  
Y. Zhou ◽  
M. Zhang
Keyword(s):  
Logic Program ◽  
Answer Set Programming ◽  
Irrelevant Information ◽  
Semantic Knowledge ◽  
Decision Problems ◽  
Stable Model ◽  
Logic Programs ◽  
Knowledge Based ◽  
Substitution Principle ◽  
Answer Set

The ability of discarding or hiding irrelevant information has been recognized as an important feature for knowledge based systems, including answer set programming. The notion of strong equivalence in answer set programming plays an important role for different problems as it gives rise to a substitution principle and amounts to knowledge equivalence of logic programs. In this paper, we uniformly propose a semantic knowledge forgetting, called HT- and FLP-forgetting, for logic programs under stable model and FLP-stable model semantics, respectively. Our proposed knowledge forgetting discards exactly the knowledge of a logic program which is relevant to forgotten variables. Thus it preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same variables. We show that this semantic forgetting result is always expressible; and we prove a representation theorem stating that the HT- and FLP-forgetting can be precisely characterized by Zhang-Zhou's four forgetting postulates under the HT- and FLP-model semantics, respectively. We also reveal underlying connections between the proposed forgetting and the forgetting of propositional logic, and provide complexity results for decision problems in relation to the forgetting. An application of the proposed forgetting is also considered in a conflict solving scenario.

scholarly journals Minish HAT: A Tool for the Minimization of Here-and-There Logic Programs and Theories in Answer Set Programming

Proceedings ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 22
Author(s):  
Rodrigo Martin ◽  
Pedro Cabalar
Keyword(s):  
Logic Program ◽  
Answer Set Programming ◽  
Boolean Logic ◽  
Minimal Representation ◽  
Logic Programs ◽  
Minimization Methods ◽  
Programming Techniques ◽  
Software Implementations ◽  
Reduced Time ◽  
Answer Set

When it comes to the writing of a new logic program or theory, it is of great importance to obtain a concise and minimal representation, for simplicity and ease of interpretation reasons. There are already a few methods and many tools, such as Karnaugh Maps or the Quine-McCluskey method, as well as their numerous software implementations, that solve this minimization problem in Boolean logic. This is not the case for Here-and-There logic, also called three-valued logic. Even though there are theoretical minimization methods for logic theories and programs, there aren’t any published tools that are able to obtain a minimal equivalent logic program. In this paper we present the first version of a tool called that is able to efficiently obtain minimal and equivalent representations for any logic program in Here-and-There. The described tool uses an hybrid method both leveraging a modified version of the Quine-McCluskey algorithm and Answer Set Programming techniques to minimize fairly complex logic programs in a reduced time.

scholarly journals Optimizing Answer Set Computation via Heuristic-Based Decomposition

2019 ◽  
Vol 19 (04) ◽  
pp. 603-628 ◽  
Author(s):  
FRANCESCO CALIMERI ◽  
SIMONA PERRI ◽  
JESSICA ZANGARI
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Answer Set Programming ◽  
Decomposition Techniques ◽  
Logic Programs ◽  
Experimental Activity ◽  
Performance Of Systems ◽  
Answer Sets ◽  
The Impact ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and non-monotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP systemDLV, in particular into its grounding subsystemℐ-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal.

A Roadmap on Updates

2011 ◽  
pp. 1370-1375
Author(s):  
Fernando Zacarías Flores ◽  
Dionicio Zacarías Flores ◽  
Rosalba Cuapa Canto ◽  
Luis Miguel Guzmán Muñoz
Keyword(s):  
Standard Model ◽  
Logic Programming ◽  
Structural Properties ◽  
Relational Databases ◽  
Logic Program ◽  
Answer Set Programming ◽  
Central Issue ◽  
The Standard Model ◽  
Answer Set

Updates, is a central issue in relational databases and knowledge databases. In the last years, it has been well studied in the non-monotonic reasoning paradigm. Several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997), (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). However, recently a set of proposals has been characterized to propose mechanisms of updates based on logic and logic programming. All these mechanisms are built on semantics based on structural properties (Eiter, Fink, Sabattini & Thompits, 2000) (Leite, 2002) (Banti, Alferes & Brogi, 2003) (Zacarias, 2005). Furthermore, all these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in (De Schreye, Hermenegildo, & Pereira, 1999).

Program completion in the input language of GRINGO

2017 ◽  
Vol 17 (5-6) ◽  
pp. 855-871 ◽  
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ ◽  
DHANANJAY RAJU
Keyword(s):  
Reverse Engineering ◽  
Large Class ◽  
Logic Program ◽  
Answer Set Programming ◽  
Program Completion ◽  
Engineering Process ◽  
Input Language ◽  
Definition Of ◽  
Answer Set

AbstractWe 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.

scholarly journals Inconsistency Proofs for ASP: The ASP - DRUPE Format

2019 ◽  
Vol 19 (5-6) ◽  
pp. 891-907
Author(s):  
MARIO ALVIANO ◽  
CARMINE DODARO ◽  
JOHANNES K. FICHTE ◽  
MARKUS HECHER ◽  
TOBIAS PHILIPP ◽  
...  
Keyword(s):  
Logic Program ◽  
Answer Set Programming ◽  
Boolean Satisfiability ◽  
Logic Programs ◽  
Disjunctive Logic Programs ◽  
Normal Logic ◽  
Consistency Problem ◽  
Unit Propagation ◽  
Answer Sets ◽  
Answer Set

AbstractAnswer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs.

scholarly journals Anytime Computation of Cautious Consequences in Answer Set Programming

2014 ◽  
Vol 14 (4-5) ◽  
pp. 755-770 ◽  
Author(s):  
MARIO ALVIANO ◽  
CARMINE DODARO ◽  
FRANCESCO RICCA
Keyword(s):  
Logic Program ◽  
Answer Set Programming ◽  
Query Answering ◽  
Anytime Algorithms ◽  
Reasonable Time ◽  
Answer Set

AbstractQuery answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.

scholarly journals Towards automated integration of guess and check programs in answer set programming: a meta-interpreter and applications

2006 ◽  
Vol 6 (1-2) ◽  
pp. 23-60 ◽  
Author(s):  
THOMAS EITER ◽  
AXEL POLLERES
Keyword(s):  
Problem Solving ◽  
Logic Program ◽  
Answer Set Programming ◽  
Polynomial Hierarchy ◽  
Logic Programs ◽  
Complete Problems ◽  
Polynomial Size ◽  
Disjunctive Logic Programs ◽  
Np Complete ◽  
Answer Set

Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise and intuitive way, where the encoding reflects the typical “guess and check” nature of NP problems: The property is encoded in a way such that polynomial size certificates for it correspond to stable models of a program. However, the problem-solving capacity of full disjunctive logic programs (DLPs) is beyond NP, and captures a class of problems at the second level of the polynomial hierarchy. While these problems also have a clear “guess and check” structure, finding an encoding in a DLP reflecting this structure may sometimes be a non-obvious task, in particular if the “check” itself is a co-NP-complete problem; usually, such problems are solved by interleaving separate guess and check programs, where the check is expressed by inconsistency of the check program. In this paper, we present general transformations of head-cycle free (extended) disjunctive logic programs into stratified and positive (extended) disjunctive logic programs based on meta-interpretation techniques. The answer sets of the original and the transformed program are in simple correspondence, and, moreover, inconsistency of the original program is indicated by a designated answer set of the transformed program. Our transformations facilitate the integration of separate “guess” and “check” programs, which are often easy to obtain, automatically into a single disjunctive logic program. Our results complement recent results on meta-interpretation in ASP, and extend methods and techniques for a declarative “guess and check” problem solving paradigm through ASP.

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