Most recently, Answer Set Programming (ASP) is attracting interest as a new paradigm for problem solving. An important aspect which needs to be supported is the handling of preferences between rules, for which several approaches have been presented. In this paper, we consider the problem of implementing preference handling approaches by means of meta-interpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable meta-interpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a meta-interpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced meta-interpreters, which make use of graph-based characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledge-representation formalisms.
We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference are too weak in the setting of well-founded semantics. We then specify some informal yet intuitive criteria and propose a semantical framework for preference handling that is more suitable for defining well-founded semantics for ordered logic programs. The suitability of the new approach is convinced by the fact that many attractive properties are satisfied b…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjuncti…
Universität Leipzig（莱比锡大学）；TU Dresden（德累斯顿工业大学）；TU Wien（维也纳工业大学）
Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labelled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this pa…
We present a declarative language, PP, for the high-level specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express non-trivial, multi-dimensional preferences and priorities over such preferences. The semantics of PP allows the identification of most preferred trajectories for a given goal. We also provide an answer set programming implementation of planning problems with PP preferences.
Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）；Universidad de las Américas - Puebla（普埃布拉美洲大学）
Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t. AF. In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an…
Dung's abstract framework for argumentation enables a study of the interactions between arguments based solely on an ``attack'' binary relation on the set of arguments. Various ways to solve conflicts between contradictory pieces of information have been proposed in the context of argumentation, nonmonotonic reasoning or logic programming, and can be captured by appropriate semantics within Dung's framework. A common feature of these semantics is that one can always maximize in some sense the set of acceptable arguments. We propose in this paper to extend Dung's framework in order to allow for…
University of Helsinki（赫尔辛基大学）；Graz University of Technology（格拉茨工业大学）
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly studied logic programming fragment of ABA. In this work, we harness recent advances in incremental ASP solving for developing effective algorithms for reasoning tasks in the logic programming fragment of ABA that are presumably hard for the second level of the polynomial hierarchy, including skeptical reasoning under preferred semantics as well as preferential r…
This paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, called Learning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples as ordered pairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) are preferred to others. In this new learning task inductive solutions are searched within a hypo…
ICLP is the premier international event for presenting research in logic programming. Contributions to ICLP 2022 were sought in all areas of logic programming, including but not limited to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages issues: Concurrency, Objects, Coordination, Mobility, Higher order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming techniques. Programming support: Program analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualiz…
ICLP is the premier international event for presenting research in logic programming. Contributions to ICLP 2021 were sought in all areas of logic programming, including but not limited to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages issues: Concurrency, Objects, Coordination, Mobility, Higher order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming techniques. Programming support: Program analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualiz…
This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given by a set of dedicated atoms. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed theory correspond with the preferred answer sets of the original theory. Since the result of the translation is an extended logic program, existing logi…
University of Huddersfield（哈德斯菲尔德大学）；Cardiff University（卡迪夫大学）；Università degli Studi di Brescia（布雷西亚大学）
Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or preferred extensions in abstract argumentation. Finding the optimum among many admissible solutions is often harder than finding admissible solutions with respect to both computational complexity and methodology. This paper addresses the former issue by means of an effective method for finding subset-optimal solutions. It is based on the relationship between car…
Institut für Logic and Computation（逻辑与计算研究所）；Technische Universität Wien（维也纳技术大学）；Marmara University（马尔马拉大学）
We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We represent this reasoning problem in Answer Set Programming (ASP), in order to obtain a flexible framework for experimenting with global constraints and objective functions, and to test the boundaries of what is possible with ASP. Realizing this problem in ASP is challenging as it requires value invention and equivalence between certain constants, because the Unique…
The Academic College of Tel-Aviv（特拉维夫学术学院）；Katholieke Universiteit Leuven（鲁汶大学）
We introduce an abductive method for a coherent integration of independent data-sources. The idea is to compute a list of data-facts that should be inserted to the amalgamated database or retracted from it in order to restore its consistency. This method is implemented by an abductive solver, called Asystem, that applies SLDNFA-resolution on a meta-theory that relates different, possibly contradicting, input databases. We also give a pure model-theoretic analysis of the possible ways to `recover' consistent data from an inconsistent database in terms of those models of the database that exhibi…
Institute of Information Systems（信息系统研究所）；Vienna University of Technology（维也纳工业大学）
Dung's famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on implementations for these frameworks, whereby one of the main approaches is to use Answer-Set Programming (ASP). While some of the argumentation semantics can be nicely expressed within the ASP language, others required rather cumbersome encoding techniques. Recent advances in ASP systems, in particular, the metasp optimization frontend for the ASP-package gr…
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 …
TU Darmstadt（达姆施塔特工业大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；Eindhoven University of Technology（埃因霍温理工大学）；German Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）
Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are sought in all areas of logic programming, including but not restricted to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming Techniques. Declarative programming: Declarative program development, Analysis, Type and mode infere…
ConArg is a Constraint Programming-based tool that can be used to model and solve different problems related to Abstract Argumentation Frameworks (AFs). To implement this tool we have used JaCoP, a Java library that provides the user with a Finite Domain Constraint Programming paradigm. ConArg is able to randomly generate networks with small-world properties in order to find conflict-free, admissible, complete, stable grounded, preferred, semi-stable, stage and ideal extensions on such interaction graphs. We present the main features of ConArg and we report the performance in time, showing als…
Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are solicited in all areas of logic programming and related areas, including but not restricted to: - Foundations: Semantics, Formalisms, Answer-Set Programming, Non-monotonic Reasoning, Knowledge Representation. - Declarative Programming: Inference engines, Analysis, Type and mode inference, Partial evaluation, Abstract interpretation, Transformation, Validation, Verification, Debugging, Profiling, Testing, Logic-based domain-specific …
Broad application of answer set programming (ASP) for declarative problem solving requires the development of tools supporting the coding process. Program debugging is one of the crucial activities within this process. Recently suggested ASP debugging approaches allow efficient computation of possible explanations of a fault. However, even for a small program a debugger might return a large number of possible explanations and selection of the correct one must be done manually. In this paper we present an interactive query-based ASP debugging method which extends previous approaches and finds a…
Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.
Software testing is a prime factor in software industry. Besides knowing the importance of testing, only limited time is allocated for teaching it. It will be more efficient if testing is taught simultaneously with programming foundations. This integrated learning of testing techniques and programming allows the programmers to perform in a better way and this leads to the improvement of the performance of the industry progress. In this paper, a technique named ontology is introduced, it first defines the various testing process in hierarchy and define relationships among them, to share and reu…
University of Oxford（牛津大学）；KU Leuven（鲁汶大学）；Imperial College London（伦敦帝国理工学院）
Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs, (iii) new approaches for predicate invention, and (iv) the use of different technologies. We conclude by discussing current limitations of ILP and directions for future research.
Most controlled natural languages (CNLs) are processed with the help of a pipeline architecture that relies on different software components. We investigate in this paper in an experimental way how well answer set programming (ASP) is suited as a unifying framework for parsing a CNL, deriving a formal representation for the resulting syntax trees, and for reasoning with that representation. We start from a list of input tokens in ASP notation and show how this input can be transformed into a syntax tree using an ASP grammar and then into reified ASP rules in form of a set of facts. These facts…
Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic programming, are widespread declarative programming techniques. In logic programming, there is a gap between the meta-programming practice and its theory: The formalisations of meta-programming do not explicitly address its impredicativity and are not fully adequate. This article aims at overcoming this unsatisfactory situation by discussing the relevance of impredicat…
This paper provides the first program logic for homogeneous generative run-time meta-programming---using a variant of MiniML by Davies and Pfenning as its underlying meta-programming language. We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics.
This paper introduces an extension of Answer Set Programming called Preference Set Constraint Programming which is a convenient and general formalism to reason with preferences. PSC programming extends Set Constraint Programming introduced by Marek and Remmel (Marek and Remmel 2004) by introducing two types of preference set constraint atoms, measure preference set constraint atoms and pre-ordered preference set constraint atoms, which are extensions of set constraint atoms. We show that the question of whether a PSC program has a preferred stable model is CoNP-complete. We give examples of th…
University of Edinburgh（爱丁堡大学）；The Alan Turing Institute（艾伦·图灵研究所）
We introduce a new application for inductive logic programming: learning the semantics of programming languages from example evaluations. In this short paper, we explored a simplified task in this domain using the Metagol meta-interpretive learning system. We highlighted the challenging aspects of this scenario, including abstracting over function symbols, nonterminating examples, and learning non-observed predicates, and proposed extensions to Metagol helpful for overcoming these challenges, which may prove useful in other domains.
We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge (programs/proofs), but also appropriate ways of reasoning (logics/type systems). We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach. In doing so, we show that specific constructions within the meta-language can be related via bisimulation (implying path equivalence) to the type systems they correspond. …
Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic programming interpretation: the Twelf system is based on such an interpretation of LF. We consider here whether a conventional logic programming language can provide the benefits of a Twelf-like system for encoding type and proof-and-formula dependencies. In particular, we present a simple mapping from LF specifications to a set of formulas in the higher-order hered…
Meta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules, which is implemented by the Metagol system based on Prolog. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP), which may result in performance gains as a result of efficient conflict propagation. However, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX-formalism, which is an ex…
In logic programming under the answer set semantics, preferences on rules are used to choose which of the conflicting rules are applied. Many interesting semantics have been proposed. Brewka and Eiter's Principle I expresses the basic intuition behind the preferences. All the approaches that satisfy Principle I introduce a rather imperative feature into otherwise declarative language. They understand preferences as the order, in which the rules of a program have to be applied. In this paper we present two purely declarative approaches for preference handling that satisfy Principle I, and work …
Type theories, logical frameworks and meta-languages form a common foundation for designing, implementing, and reasoning about formal languages and their semantics. They are central to the design of modern programming languages, certified software, and domain specific logics. More generally, they continue to influence applications in many areas in mathematics, logic and computer science. The Logical Frameworks and Meta-languages: Theory and Practice workshop aims to bring together designers, implementers, and practitioners working on these areas, and in particular about: the automation and imp…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined using a bounded amount of auxiliary information that is independent of expression size but depends on a fixed structure over which evaluation occurs. We introduce a generic programming language for writing programs that evaluate expression syntax trees, and we give a meta-theorem that connects such programs for finite-aspect checkable languages to finite tre…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis for a broad class of practical meta-interpreters, including negation and performing different tasks during the execution. It is based on combining the power of general orderings, used in proving termination of term-rewrite systems and programs, and on the well-known acceptability condition, used in proving termination of logic programs. The methodology estab…
