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Symbolic Model Construction for Saturated Constrained Horn Clauses

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arXiv 2023年

作者： Bromberger, Martin Leutgeb, Lorenz Weidenbach, Christoph Max Planck Institute for Informatics Saarland Informatics Campus Saarbrücken Germany Graduate School of Computer Science Saarland Informatics Campus Saarbrücken Germany

Clause sets saturated by hierarchic ordered resolution do not offer a model representation that can be effectively queried, in general. They only offer the guarantee of the existence of a model. We present an effective symbolic model construction for saturated constrained Horn clauses. Constraints are in linear arithmetic, the first-order part is restricted to a function-free language. The model is constructed in finite time, and non-ground clauses can be effectively evaluated with respect to the model. Furthermore, we prove that our model construction produces the least model. Copyright © 2023, The Authors. All rights reserved.

关键词： logic programming

Sorting Strategies for Interactive Conflict Resolution in ASP

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arXiv 2023年

作者： Thevapalan, Andre Kern-Isberner, Gabriele Technische Universität Dortmund Dortmund Germany

Answer set programs in practice are often subject to change. This can lead to inconsistencies in the modified program due to conflicts between rules which are the results of the derivation of strongly complementary literals. To facilitate the maintenance of consistency in answer set programs, in this paper we continue work on a recently presented framework that implements interactive conflict resolution by extending the bodies of conflicting rules by suitable literals, so-called λ -extensions. More precisely, we present strategies to choose λ -extensions that allow for resolving several conflicts at a time in an order that aims at minimizing (cognitive) efforts. In particular, we present a graphical representation of connections between conflicts and their possible solutions. Such a representation can be utilized to efficiently guide the user through the conflict resolution process by displaying conflicts and suggesting solutions in a suitable order. © 2023, CC BY.

关键词： logic programming

Past-present temporal programs over finite traces

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arXiv 2023年

作者： Cabalar, Pedro Diéguez, Martín Laferrière, François Schaub, Torsten University of Corunna Spain University of Angers France University of Potsdam Germany

Extensions of Answer Set programming with language constructs from temporal logics, such as temporal equilibrium logic over finite traces (TELf), provide an expressive computational framework for modeling dynamic applications. In this paper, we study the so-called past-present syntactic subclass, which consists of a set of logic programming rules whose body references to the past and head to the present. Such restriction ensures that the past remains independent of the future, which is the case in most dynamic domains. We extend the definitions of completion and loop formulas to the case of past-present formulas, which allows for capturing the temporal stable models of past-present temporal programs by means of an LTLf expression. Copyright © 2023, The Authors. All rights reserved.

关键词： logic programming

Data Validation Meets Answer Set programming 23rd

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Data Validation Meets Answer Set Programming

23rd International Symposium on Practical Aspects of Declarative Languages, PADL 2021

作者： Alviano, Mario Dodaro, Carmine Zamayla, Arnel Department of Mathematics and Computer Science University of Calabria Via P. Bucci cubo 30B RendeCS87036 Italy

ISBN: (纸本)9783030674373

Data validation may save the day of computer programmers, whatever programming language they use. In fact, processing invalid data is a waste of resources at best, and a drama at worst if the problem remains unnoticed and wrong results are used for business. Answer Set programming is not an exception, but the quest for better and better performance resulted in systems that essentially do not validate data in any way. Even under the simplistic assumption that input and output data are eventually validated by external tools, invalid data may appear in other portions of the program, and go undetected until some other module of the designed software suddenly breaks. This paper formalizes the problem of data validation for ASP programs, introduces a declarative language to specify data validation, and presents a tool to inject data validation in ordinary programs. The proposed approach promotes fail-fast techniques at coding time without imposing any lag on the deployed system if data are pretended to be valid. Additionally, the proposed approach opens the possibility to take advantage of ASP declarativity for validating complex data of imperative programming languages. © 2021, Springer Nature Switzerland AG.

关键词： logic programming

smProbLog: Stable Model Semantics in ProbLog for Probabilistic Argumentation

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arXiv 2023年

作者： Totis, Pietro de Raedt, Luc Kimmig, Angelika KU Leuven Dept. of Computer Science Leuven.AI LeuvenB-3000 Belgium

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics, which is, that probabilistic facts fully capture the uncertainty in the domain under investigation. The second contribution of this paper is then a novel PLP semantics for programs where a choice of probabilistic facts does not uniquely determine the truth assignment of the logical atoms. The third contribution of this paper is the implementation of a PLP system supporting this semantics: smProbLog. smProbLog is a novel PLP framework based on the probabilistic logic programming language ProbLog. smProbLog supports many inference and learning tasks typical of PLP, which, together with our first contribution, provide novel reasoning tools for probabilistic argumentation. We evaluate our approach with experiments analyzing the computational cost of the proposed algorithms and their application to a dataset of argumentation problems. Under consideration in Theory and Practice of logic programming (TPLP).MSC Codes 68-06, 68T30 Copyright © 2023, The Authors. All rights reserved.

关键词： logic programming

Full Automation of Goal-driven LLM Dialog Threads with And-Or Recursors and Refiner Oracles

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arXiv 2023年

作者： Tarau, Paul University of North Texas United States

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature. © 2023, CC BY.

关键词： logic programming

Intelligent query answering with contextual knowledge for relational databases 10

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Intelligent query answering with contextual knowledge for re...

10th Symposium on Languages, Applications and Technologies, SLATE 2021

作者： Seipel, Dietmar Weidner, Daniel Abreu, Salvador Department of Computer Science Universität Würzburg Germany Nova-Lincs University of Évora Portugal

ISBN: (纸本)9783959772020

We are proposing a keyword-based query interface for knowledge bases - including relational or deductive databases - based on contextual background knowledge such as suitable join conditions or synonyms. Join conditions could be extracted from existing referential integrity (foreign key) constaints of the database schema. They could also be learned from other, previous database queries, if the database schema does not contain foreign key constraints. Given a textual representation - a word list - of a query to a relational database, one may parse the list into a structured term. The intelligent and cooperative part of our approach is to hypothesize the semantics of the word list and to find suitable links between the concepts mentioned in the query using contextual knowledge, more precisely join conditions between the database tables. We use a knowledge-based parser based on an extension of Definite Clause Grammars (Dcg) that are interweaved with calls to the database schema to suitably annotate the tokens as table names, table attributes, attribute values or relationships linking tables. Our tool DdQl yields the possible queries in a special domain specific rule language that extends Datalog, from which the user can choose one. © 2021 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： logic programming

Exp(ASPc): Explaining ASP programs with choice atoms and constraint rules 37

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Exp(ASPc): Explaining ASP programs with choice atoms and con...

37th International Conference on logic programming (Technical Communications), ICLP 2021

作者： Trieu, Ly Ly Son, Tran Cao Balduccini, Marcello New Mexico State University New Mexico United States Saint Joseph's University Pennsylvania United States

We present an enhancement of exp(ASP), a system that generates explanation graphs for a literal-an atom a or its default negation ∼ a-given an answer set A of a normal logic program P, which explain why ` is true (or false) given A and P. The new system, exp(ASPc), differs from exp(ASP) in that it supports choice rules and utilizes constraint rules to provide explanation graphs that include information about choices and constraints. © L.L. Trieu, T.C. Son & M. Balduccini This work is licensed under the Creative Commons Attribution License.

关键词： logic programming

Game Semantics for Non-monotonic Intensional logic programming

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Game Semantics for Non-monotonic Intensional Logic Programmi...

12th International Conference on logic programming and Nonmonotonic Reasoning (LPNMR)

作者： Galanaki, Chrysida Nomikos, Christos Rondogiannis, Panos Univ Athens Dept Informat & Telecommun GR-10679 Athens Greece Univ Ioannina Dept Comp Sci & Engn GR-45110 Ioannina Greece

ISBN: (纸本)9783642405648

Intensional logic programming is an extension of logic programming based on intensional logic, which includes as special cases both temporal and modal logic programming. In [OW92], M. Orgun and W. W. Wadge provided a general framework for capturing the semantics of intensional logic programming languages. One key property involved in the construction of [OW92], is the monotonicity of intensional operators. In this paper we consider intensional logic programming from a game-theoretic perspective. In particular we define a two-person game and we demonstrate that it is equivalent to the semantics of [OW92]. More importantly, we demonstrate that the game is even applicable to intensional languages with non-monotonic operators. In this way we provide the first (to our knowledge) general semantic framework for capturing the semantics of non-monotonic intensional logic programming.

关键词： logic programming