V. W. Marek, J. B. Remmel
We apply proof-theoretic techniques in answer Set Programming. The main results include: 1. A characterization of continuity properties of Gelfond-Lifschitz operator for logic program. 2. A propositional characterization of stable models of logic programs (without referring to loop formulas.
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This is the Proceedings of the twelfth Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP) 2019, which was held in Philadelphia, USA, June 3rd , 2019.
Recent progress in logic programming (e.g., the development of the Answer Set Programming 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 answer set programming environment with a self contained file system and a simple interface. It allows users to type/edit logic programs a…
We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as smodels and dlv is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelae is discussed as an example.
We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and for learning of such weights from data (parameter estimation). Weighted formulas are given a semantics in terms of soft and hard constraints which determine a probability distribution over answer sets. In contrast to related approaches, we approach inference by optionally utilizing so-called streamlining XOR constraints, in order to reduce the number of comp…
Reactive answer set programming has paved the way for incorporating online information into operative solving processes. Although this technology was originally devised for dealing with data streams in dynamic environments, like assisted living and cognitive robotics, it can likewise be used to incorporate facts, rules, or queries provided by a user. As a result, we present the design and implementation of a system for interactive query answering with reactive answer set programming. Our system quontroller is based on the reactive solver oclingo and implemented as a dedicated front-end. We des…
Functional Stable Model Semantics and Answer Set Programming Modulo Theories
本文探讨了在答案集编程中整合'intensional'函数的作用，展示了功能稳定模型语义在ASPMT框架中的关键作用，并证明了紧致ASPMT程序可转换为SMT实例。
We allow representing and reasoning in the presence of nested multiple aggregates over multiple variables and nested multiple aggregates over functions involving multiple variables in answer sets, precisely, in answer set optimization programming and in answer set programming. We show the applicability of the answer set optimization programming with nested multiple aggregates and the answer set programming with nested multiple aggregates to the Probabilistic Traveling Salesman Problem, a fundamental a priori optimization problem in Operation Research.
This volume contains the papers presented at the fifth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2012) held on September 4th, 2012 in Budapest, co-located with the 28th International Conference on Logic Programming (ICLP 2012). It thus continues a series of previous events co-located with ICLP, aiming at facilitating the discussion about crossing the boundaries of current ASP techniques in theory, solving, and applications, in combination with or inspired by other computing paradigms.
We describe a variant of resolution rule of proof and show that it is complete for stable semantics of logic programs. We show applications of this result.
Query 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.
Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo theories. Constraint answer set programming demonstrates promising results, including the development of a multitude of solvers: acsolver, clingcon, ezcsp, idp, inca, dingo, mingo, aspmt, clingo[l,dl], and ezsmt. It opens new horizons for declarative programming applications such as solving complex train scheduling problems. Systems designed to find solutions to…
We discuss the evolution of aspects of nonmonotonic reasoning towards the computational paradigm of answer-set programming (ASP). We give a general overview of the roots of ASP and follow up with the personal perspective on research developments that helped verbalize the main principles of ASP and differentiated it from the classical logic programming.
We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the context of the logic of Here-and-There and show how it can be derived from the logical principle of extension by definition. We then provide an austere form of logic programs that may serve as a normalform for logic programs similar to conjunctive normalform in classical logic. Finally, we take the key ideas and propose a modeling methodology for ASP beginner…
Fuzzy answer set programming is a declarative framework for representing and reasoning about knowledge in fuzzy environments. However, the unavailability of fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer set semantics prohibits the natural and concise representation of many interesting problems. In this paper, we extend DFLP to allow arbitrary fuzzy aggregates. We define fuzzy answer set semantics for DFLP with arbitrary fuzzy aggregates including monotone, antimonotone, and nonmonotone fuzzy aggregates. We show that the proposed fuzzy answer set semantics subsum…
A belief base revision is developed. The belief base is represented using Unified Answer Set Programs which is capable of representing imprecise and uncertain information and perform nonomonotonic reasoning with them. The base revision operator is developed using Removed Set Revision strategy. The operator is characterized with respect to the postulates for base revisions operator satisfies.
We present an explanation system for applications that leverage Answer Set Programming (ASP). Given a program P, an answer set A of P, and an atom a in the program P, our system generates all explanation graphs of a which help explain why a is true (or false) given the program P and the answer set A. We illustrate the functionality of the system using some examples from the literature.
Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty. While such an extension is important from an application point of view, existing semantics are not well-motivated, and do not always yield intuitive results. To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints on possibility distributions. This characterization is then naturally generalized to define answer sets of PASP…
This volume contains the papers presented at the sixth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2013) held on August 25th, 2013 in Istanbul, co-located with the 29th International Conference on Logic Programming (ICLP 2013). It thus continues a series of previous events co-located with ICLP, aiming at facilitating the discussion about crossing the boundaries of current ASP techniques in theory, solving, and applications, in combination with or inspired by other computing paradigms.
Answer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on Logic Programming and Non-Mo…
We provide a semantic framework for preference handling in answer set programming. To this end, we introduce preference preserving consequence operators. The resulting fixpoint characterizations provide us with a uniform semantic framework for characterizing preference handling in existing approaches. Although our approach is extensible to other semantics by means of an alternating fixpoint theory, we focus here on the elaboration of preferences under answer set semantics. Alternatively, we show how these approaches can be characterized by the concept of order preservation. These uniform seman…
Probabilistic Answer Set Programming with Discrete and Continuous Random Variables
针对PASP仅支持离散随机变量的局限，本文提出HPASP框架以结合离散与连续变量，实现并评估两类精确算法（投影枚举、知识编译）和两类近似采样算法，发现知识编译提升精确推理性能，采样适用于大实例。
We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. Our example is a formalism aiming at capturing causal explanations from causal information. We show the naturalness and relative efficiency of this translation job. We are interested in the ease for writing an ASP program. Limitations of the earlier systems made that in practice, the ``declarative aspect'' was more theoretical than practical. We show how recent improvements in working ASP systems facilitate the translation.
This paper describes an approach to the methodology of answer set programming (ASP) that can facilitate the design of encodings that are easy to understand and provably correct. Under this approach, after appending a rule or a small group of rules to the emerging program we include a comment that states what has been "achieved" so far. This strategy allows us to set out our understanding of the design of the program by describing the roles of small parts of the program in a mathematically precise way.
PDDL+ is an extension of PDDL that enables modelling planning domains with mixed discrete-continuous dynamics. In this paper we present a new approach to PDDL+ planning based on Constraint Answer Set Programming (CASP), i.e. ASP rules plus numerical constraints. To the best of our knowledge, ours is the first attempt to link PDDL+ planning and logic programming. We provide an encoding of PDDL+ models into CASP problems. The encoding can handle non-linear hybrid domains, and represents a solid basis for applying logic programming to PDDL+ planning. As a case study, we consider the EZCSP CASP so…
Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of probability aggregates; a type that computes the expected value of a classical aggregate, e.g., the expe…
A introduction to the syntax and Semantics of Answer Set Programming intended as an handout to [under]graduate students taking Artificial Intlligence or Logic Programming classes.
Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models is not trivial. We propose a novel method, called Sketched Answer Set Programming (SkASP), aiming at supporting the user in resolving this issue. The user writes an ASP program while marking uncertain parts open with question marks. In addition, the user provides a number of positive and negative examples of the desired program behaviour. The sketched model is rewritten into another ASP program, which is solved by traditional methods. As a result, the user obtains a functional …
Logic Production System (LPS) is a logic-based framework for modelling reactive behaviour. Based on abductive logic programming, it combines reactive rules with logic programs, a database and a causal theory that specifies transitions between the states of the database. This paper proposes a systematic mapping of the Kernel of this framework (called KELPS) into an answer set program (ASP). For this purpose a new variant of KELPS with finite models, called $n$-distance KELPS, is introduced. A formal definition of the mapping from this $n$-distance KELPS to ASP is given and proven sound and comp…
For a finite state automaton, a synchronizing sequence is an input sequence that takes all the states to the same state. Checking the existence of a synchronizing sequence and finding a synchronizing sequence, if one exists, can be performed in polynomial time. However, the problem of finding a shortest synchronizing sequence is known to be NP-hard. In this work, the usefulness of Answer Set Programming to solve this optimization problem is investigated, in comparison with brute-force algorithms and SAT-based approaches. Keywords: finite automata, shortest synchronizing sequence, ASP
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…
Explanations for Answer Set Programming
本文提出xASP2系统，扩展了xASP以支持更多clingo结构，通过缩小假设集并生成有向无环图解释，增强ASP的可解释性。
Meta-Programming for Linear-time Temporal Answer Set Programming
提出一种统一的元编程框架，通过扩展clingo的理论语法并引入转换管道保护嵌套模态，实现了对多种线性时态逻辑（TEL、MEL、DEL）的语义操作化，并开发了metasp系统。
The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor. In this paper, we present new encodings for three prominent argumentation semantics using the concept of conditional literals in disjunctions as provided by the ASP-system clingo. Our new encodings are not only more succinct than previous versions, but also outperform them on standard benchmarks.
Using Answer Set Programming in an Inference-Based approach to Natural Language Semantics
The advance of Internet and Sensor technology has brought about new challenges evoked by the emergence of continuous data streams. Beyond rapid data processing, application areas like ambient assisted living, robotics, or dynamic scheduling involve complex reasoning tasks. We address such scenarios and elaborate upon approaches to knowledge-intense stream reasoning, based on Answer Set Programming (ASP). While traditional ASP methods are devised for singular problem solving, we develop new techniques to formulate and process problems dealing with emerging as well as expiring data in a seamless…
We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the sc…
Artificial Intelligence (AI) approaches to problem-solving and decision-making are becoming more and more complex, leading to a decrease in the understandability of solutions. The European Union's new General Data Protection Regulation tries to tackle this problem by stipulating a "right to explanation" for decisions made by AI systems. One of the AI paradigms that may be affected by this new regulation is Answer Set Programming (ASP). Thanks to the emergence of efficient solvers, ASP has recently been used for problem-solving in a variety of domains, including medicine, cryptography, and biol…
We present a solution to real-world train scheduling problems, involving routing, scheduling, and optimization, based on Answer Set Programming (ASP). To this end, we pursue a hybrid approach that extends ASP with difference constraints to account for a fine-grained timing. More precisely, we exemplarily show how the hybrid ASP system clingo[DL] can be used to tackle demanding planning-and-scheduling problems. In particular, we investigate how to boost performance by combining distinct ASP solving techniques, such as approximations and heuristics, with preprocessing and encoding techniques for…
Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. We define a fixed point logic (FPL) extension of Clark's completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (mu(L)GF). Moreover, we reduce normal closed ASP t…
Answer Set Programming Energised! End-to-End Neurosymbolic Reasoning and Learning with ASP and Energy Based Models
该研究提出基于Answer Set编程与能量模型集成的神经符号推理学习方法，通过显式语义支持联合优化，纳入背景知识等，还提供通用模型和平台用于动态领域训练，经实际实现及在MNIST、Clevr、MOT上的测试评估其效果。
Answer Set Programming Modulo Theories and Reasoning about Continuous Changes
本文提出ASPMT框架，将答案集编程与SMT紧密集成，并通过增强动作语言C+展示其在连续与离散变化推理及连续资源累积效应表示中的有效性。
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…
In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot ASP systems and benefits from an extension of ASP's full-fledged input language with temporal operators. This in…
Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka et al. KR 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A \times B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. LPODs are useful for applications …
We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Unlike previous approaches to belief change in logic programming, our formal techniques are analogous to those of distance-based belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic characterisation of logic programs, we can adapt techniques from the area of belief revision to belief change in logic programs. We introduce methods for revising and merging logic pr…
In this paper we present an Action Language-Answer Set Programming based approach to solving planning and scheduling problems in hybrid domains - domains that exhibit both discrete and continuous behavior. We use action language H to represent the domain and then translate the resulting theory into an A-Prolog program. In this way, we reduce the problem of finding solutions to planning and scheduling problems to computing answer sets of A-Prolog programs. We cite a planning and scheduling example from the literature and show how to model it in H. We show how to translate the resulting H theory…
We present an implementation of an answer-set programming paradigm, called aspps (short for answer-set programming with propositional schemata). The system aspps is designed to process PS+ theories. It consists of two basic modules. The first module, psgrnd, grounds an PS+ theory. The second module, referred to as aspps, is a solver. It computes models of ground PS+ theories.
In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem …
This paper explores the contributions of Answer Set Programming (ASP) to the study of an established theory from the field of Second Language Acquisition: Input Processing. The theory describes default strategies that learners of a second language use in extracting meaning out of a text, based on their knowledge of the second language and their background knowledge about the world. We formalized this theory in ASP, and as a result we were able to determine opportunities for refining its natural language description, as well as directions for future theory development. We applied our model to a…
A Proof-of-Concept for Explainable Disease Diagnosis Using Large Language Models and Answer Set Programming
本研究提出McCoy框架，结合大型语言模型与答案集编程，实现可解释的疾病诊断，初步结果显示其在小规模诊断任务中表现优异。
One of our long term research goals is to develop systems to answer realistic questions (e.g., some mentioned in textbooks) about biological pathways that a biologist may ask. To answer such questions we need formalisms that can model pathways, simulate their execution, model intervention to those pathways, and compare simulations under different circumstances. We found Petri Nets to be the starting point of a suitable formalism for the modeling and simulation needs. However, we need to make extensions to the Petri Net model and also reason with multiple simulation runs and parallel state evol…
This is the Proceedings of the eleventh Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP) 2018, which was held in Oxford, UK, July 18th, 2018.
In recent years, Answer Set Programming (ASP), logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be it aggregate atoms, HEX atoms, generalized quantifiers, or abstract constraints, the idea is to have more complicated satisfaction patterns in the lattice of Herbrand interpretations than traditional, simple atoms. In this paper we refer to any of these constructs as generalized atoms. Several semantics with differing characteristics have been proposed for these extensions, rendering the big pict…
The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domain-restricted but supports extensions including built-in functions as well as cardinality and weight constraints. On top of this core engine more involved systems can be built. As an example, we have implemented total and partial stable model computation for disjunctive logic programs. An interesting application method is based on answer set programming, i.e., encoding an application problem as a set of rules so that its solutions a…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable assignments or answer sets) subject to user-provided probabilistic constraints. The sampling process minimizes a user-defined differentiable objective function using a gradient descent based optimization method called Differentiable Satisfiability Solving ($\partial\mathrm{SAT}$) respectively Differentiable Answer Set Programming ($\partial\mathrm{ASP}$). Use cas…
Distilling Answer-Set Programming Rules from LLMs for Neurosymbolic Visual Question Answering
提出从大语言模型中蒸馏答案集编程规则的方法，以可解释的方式扩展视觉问答系统的推理能力，仅需少量示例即可生成正确规则。
We propose a method for generating explainable rule sets from tree-ensemble learners using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract interesting rules. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand th…
The goal of combining the robustness of neural networks and the expressivity of symbolic methods has rekindled the interest in neuro-symbolic AI. Recent advancements in neuro-symbolic AI often consider specifically-tailored architectures consisting of disjoint neural and symbolic components, and thus do not exhibit desired gains that can be achieved by integrating them into a unifying framework. We introduce SLASH -- a novel deep probabilistic programming language (DPPL). At its core, SLASH consists of Neural-Probabilistic Predicates (NPPs) and logical programs which are united via answer set …
Gelfond and Zhang recently proposed a new stable model semantics based on Vicious Circle Principle in order to improve the interpretation of logic programs with aggregates. The paper focuses on this proposal, and analyzes the complexity of both coherence testing and cautious reasoning under the new semantics. Some surprising results highlight similarities and differences versus mainstream stable model semantics for aggregates. Moreover, the paper reports on the design of compilation techniques for implementing the new semantics on top of existing ASP solvers, which eventually lead to realize a…
Answering realistic questions about biological systems and pathways similar to the ones used by text books to test understanding of students about biological systems is one of our long term research goals. Often these questions require simulation based reasoning. To answer such questions, we need formalisms to build pathway models, add extensions, simulate, and reason with them. We chose Petri Nets and Answer Set Programming (ASP) as suitable formalisms, since Petri Net models are similar to biological pathway diagrams; and ASP provides easy extension and strong reasoning abilities. We found t…
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