Abductive Logic Programming Research Articles

An efficient propositional system for Abductive Logic Programming

Abductive logic programming (ALP) extends logic programming with hypothetical reasoning by means of abducibles, an extension able to handle interesting problems, such as diagnosis, planning, and verification with formal methods. Implementations of this extension have been using Prolog meta-interpreters and Prolog programs with Constraint Handling Rules (CHR). While the latter adds a clean and efficient interface to the host system, it still suffers in performance for large programs. Here, the concern is to obtain a more performant implementation of the SCIFF system following a compiled approach. This paper, as a first step in this long term goal, sets out a propositional ALP system following SCIFF, eliminating the need for CHR and achieving better performance.

Computing Abductive Explanations

We study the computation of constrained explanations in the framework of abductive logic programming. A general characteristic of abductive reasoning is the existence of multiple abductive explanations. Therefore, identifying a subclass of “preferred explanations” is a relevant problem. A typical approach is to “prefer” explanations that are, in some sense, simple. Several concepts of simplicity were considered in the literature, most notably those based on minimality with respect to inclusion and cardinality. We adopt, as a measure of the quality of an explanation, its degree of arbitrariness that can be briefly described as the number of arbitrary assumptions that have been made to derive the explanation. The more arbitrary the explanation, the less appealing it is, with explanations having no arbitrariness, called constrained, being the preferred ones. In this article, we present a technique that, for a special class of theories, computes constrained explanations. It is based on a rewriting of the theory and the observation into a disjunctive logic program with negation so that the constrained explanations correspond to a subset of its stable models. The proposed technique lays the foundation for using ASP solvers to compute constrained explanations.

Reactive Answer Set Programming

AbstractLogic 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, calledn-distance KELPS, is introduced. A formal definition of the mapping from thisn-distance KELPS to ASP is given and proven sound and complete. The Answer Set Programming paradigm allows to capture additional behaviours to the basic reactivity of KELPS, in particular proactive, pre-emptive and prospective behaviours. These are all discussed and illustrated with examples. Then a hybrid framework is proposed that integrates KELPS and ASP, allowing to combine the strengths of both paradigms.

Abduction with probabilistic logic programming under the distribution semantics

In Probabilistic Abductive Logic Programming we are given a probabilistic logic program, a set of abducible facts, and a set of constraints. Inference in probabilistic abductive logic programs aims to find a subset of the abducible facts that is compatible with the constraints and that maximizes the joint probability of the query and the constraints. In this paper, we extend the PITA reasoner with an algorithm to perform abduction on probabilistic abductive logic programs exploiting Binary Decision Diagrams. Tests on several synthetic datasets show the effectiveness of our approach.

Nonground Abductive Logic Programming with Probabilistic Integrity Constraints

AbstractUncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints à la IFF, possibly annotated with a probability value. We first present the overall abductive language and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.

Dischargeable Obligations in the 𝒮CIFF Framework

Abductive Logic Programming (ALP) has been proven very effective for formalizing societies of agents, commitments and norms, in particular by mapping the most common deontic operators (obligation, prohibition, permission) to abductive expectations. In our previous works, we have shown that ALP is a suitable framework for representing norms. Normative reasoning and query answering were accommodated by the same abductive proof procedure, named 𝒮CIFF. In this work, we introduce a defeasible flavour in this framework, in order to possibly discharge obligations in some scenarios. Abductive expectations can also be qualified as dischargeable, in the new, extended syntax. Both declarative and operational semantics are improved accordingly, and proof of soundness is given under syntax allowedness conditions Moreover, the dischargement itself might be proved invalid, or incoherent with the rules, due to new knowledge provided later on. In such a case, a discharged expectation might be reinstated and hold again after some evidence is given. We extend the notion of dischargement to take into consideration also the reinstatement of expectations. The expressiveness and power of the extended framework, named 𝒮CIFF𝒟, is shown by modeling and reasoning upon a fragment of the Japanese Civil Code. In particular, we consider a case study concerning manifestations of intention and their rescission (Section II of the Japanese Civil Code).

Indefinite abductive explanations

ABSTRACTThis paper stems from previous works of the authors in which a new measure of the simplicity of an explanation based on its degree of arbitrariness is proposed: The more the explanation is arbitray, the less appealing it is, with explanations having no arbitrariness – called constrained – being the preferred ones. In previous works, as commonly done in the literature of abductive logic programming, a set of hypotheses is not an explanation, unless it is definite, i.e. it explains all the data belonging to the observation. In this paper, we follow a different perspective and define the concept of indefinite constrained explanations, i.e. constrained explanations that are not definite, but admit some indefiniteness. An indefinite constrained explanation captures the intuition of the existence of an explanation (indefinite explanation) that would best explain the given evidence, while not making arbitrary choices (constrained explanation). The main contribution of the paper is the study of abduction in indefinite deductive theories: specifically, the paper studies the framework of abductive logic programming extended with integrity constraints in the setting in which both the initial knowledge base and the abductive explanations are indefinite (may contain occurrences of null values) and the domain is possibly infinite. Furthermore, the paper discusses the complexity of problems concerning indefinite (constrained) explanations.

Dr. Furukawa’s View in Using Abductive Logic Programming for Promoting Cognition

Dr. Furukawa had a sharp view in pinpointing that the crucial issue in skill science lies in discovering missing parts, that it is an act of abductive thinking, and that logic programming can be best used to encourage people, who intend to learn embodied skills, to think and feel more than without it. In the wake of the grief that our communities lost Dr. Furukawa, discussions on implications that his great contributions to AI, cognitive science and skill science have brought to us are a necessary “must” for all that keep doing researches for people’s well-being.

Extending expressivity and flexibility of abductive logic programming

Real-world problems often require purely deductive reasoning to be supported by other techniques that can cope with noise in the form of incomplete and uncertain data. Abductive inference tackles incompleteness by guessing unknown information, provided that it is compliant with given constraints. Probabilistic reasoning tackles uncertainty by weakening the sharp logical approach. This work aims at bringing both together and at further extending the expressive power of the resulting framework, called Probabilistic Expressive Abductive Logic Programming (PEALP). It adopts a Logic Programming perspective, introducing several kinds of constraints and allowing to set a degree of strength on their validity. Procedures to handle both extensions, compatibly with standard abductive and probabilistic frameworks, are also provided.

Accountable Protocols in Abductive Logic Programming

Finding the entity responsible for an unpleasant situation is often difficult, especially in artificial agent societies. S CIFF is a formalization of agent societies, including a language to describe rules and protocols, and an abductive proof procedure for compliance checking. However, how to identify the entity responsible for a violation is not always clear. In this work, a definition of accountability for artificial societies is formalized in S CIFF. Two tools are provided for the designer of interaction protocols: a guideline, in terms of syntactic features that ensure accountability of the protocol, and an algorithm (implemented in a software tool) to investigate if, for a given protocol, nonaccountability issues could arise.

Reasoning on Datalog± Ontologies with Abductive Logic Programming

Reasoning on Datalog± Ontologies with Abductive Logic Programming

Evaluating Compliance: From LTL to Abductive Logic Programming

The compliance verification task amounts to establishing if the execution of a system, given in terms of observed events, does respect a given property. In the past both the frameworks of Temporal Logics and Logic Programming have been extensively exploited to assess compliance. In this work we review the LTL and the Abductive Logic Programming frameworks in the light of compliance evaluation, and formally investigate the relationship between the two approaches. We define a notion of compliance within each approach, and then we show that an arbitrary LTL formula can be expressed in SCIFF, by providing an automatic translation procedure from LTL to SCIFF which preserves compliance.

Probabilistic abductive logic programming using Dirichlet priors

Probabilistic programming is an area of research that aims to develop general inference algorithms for probabilistic models expressed as probabilistic programs whose execution corresponds to inferring the parameters of those models. In this paper, we introduce a probabilistic programming language (PPL) based on abductive logic programming for performing inference in probabilistic models involving categorical distributions with Dirichlet priors. We encode these models as abductive logic programs enriched with probabilistic definitions and queries, and show how to execute and compile them to boolean formulas. Using the latter, we perform generalized inference using one of two proposed Markov Chain Monte Carlo (MCMC) sampling algorithms: an adaptation of uncollapsed Gibbs sampling from related work and a novel collapsed Gibbs sampling (CGS). We show that CGS converges faster than the uncollapsed version on a latent Dirichlet allocation (LDA) task using synthetic data. On similar data, we compare our PPL with LDA-specific algorithms and other PPLs. We find that all methods, except one, perform similarly and that the more expressive the PPL, the slower it is. We illustrate applications of our PPL on real data in two variants of LDA models (Seed and Cluster LDA), and in the repeated insertion model (RIM). In the latter, our PPL yields similar conclusions to inference with EM for Mallows models.

A Measure of Arbitrariness in Abductive Explanations

AbstractWe study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of arbitrariness: the more arbitrary the explanation, the less appealing it is, with explanations having no arbitrariness — they are called constrained — being the preferred ones. In the paper, we study basic properties of constrained explanations. For the case when programs in abductive theories are stratified we establish results providing a detailed picture of the complexity of the problem to decide whether constrained explanations exist.

Formalizing Negotiations Using Logic Programming

The article introduces a logical framework for negotiation among dishonest agents. The framework relies on the use of abductive logic programming as a knowledge representation language for agents to deal with incomplete information and preferences. The article shows how intentionally false or inaccurate information of agents can be encoded in the agents' knowledge bases. Such disinformation can be effectively used in the process of negotiation to have desired outcomes by agents. The negotiation processes are formulated under the answer set semantics of abductive logic programming, and they enable the exploration of various strategies that agents can employ in their negotiation. A preliminary implementation has been developed using the ASP-Prolog platform.

Using possibilistic logic for modeling qualitative decision: Answer Set Programming algorithms

A qualitative approach to decision making under uncertainty has been proposed in the setting of possibility theory, which is based on the assumption that levels of certainty and levels of priority (for expressing preferences) are commensurate. In this setting, pessimistic and optimistic decision criteria have been formally justified. This approach has been transposed into possibilistic logic in which the available knowledge is described by formulas which are more or less certainly true and the goals are described in a separate prioritized base. This paper adapts the possibilistic logic handling of qualitative decision making under uncertainty in the Answer Set Programming (ASP) setting. We show how weighted beliefs and prioritized preferences belonging to two separate knowledge bases can be handled in ASP by modeling qualitative decision making in terms of abductive logic programming where (uncertain) knowledge about the world and prioritized preferences are encoded as possibilistic definite logic programs and possibilistic literals respectively. We provide ASP-based and possibilistic ASP-based algorithms for calculating optimal decisions and utility values according to the possibilistic decision criteria. We describe a prototype implementing the algorithms proposed on top of different ASP solvers and we discuss the complexity of the different implementations.

The CHR-based Implementation of the SCIFF Abductive System

Abduction is a form of inference that supports hypothetical reasoning and has been applied to a number of domains, such as diagnosis, planning, protocol verification. Abductive Logic Programming ALP is the integration of abduction in logic programming. Usually, the operational semantics of an ALP language is defined as a proof procedure. The first implementations of ALP proof-procedures were based on the meta-interpretation technique, which is flexible but limits the use of the built-in predicates of logic programming systems. Another, more recent, approach exploits theoretical results on the similarity between abducibles and constraints. With this approach, which bears the advantage of an easy integration with built-in predicates and constraints, Constraint Handling Rules has been the language of choice for the implementation of abductive proof procedures. The first CHR-based implementation mapped integrity constraints directly to CHR rules, which is an efficient solution, but prevents defined predicates from being in the body of integrity constraints and does not allow a sound treatment of negation by default. In this paper, we describe the CHR-based implementation of the SCIFF abductive proof-procedure, which follows a different approach. The SCIFF implementation maps integrity constraints to CHR constraints, and the transitions of the proof-procedure to CHR rules, making it possible to treat default negation, while retaining the other advantages of CHR-based implementations of ALP proof-procedures.

Introduction to the 27th International Conference on Logic Programming Special Issue

Following the initiative in 2010 taken by the Association for Logic Programming and Cambridge University Press, the full papers accepted for the International Conference on Logic Programming again appear as a special issue of Theory and Practice of Logic Programming (TPLP)—the 27th International Conference on Logic Programming Special Issue. Papers describing original, previously unpublished research and not simultaneously submitted for publication elsewhere were solicited in all areas of logic programming including but not restricted to: Theory: Semantic Foundations, Formalisms, Non- monotonic Reasoning, Knowledge Representation. Implementation: Compilation, Memory Management, Virtual Machines, Parallelism. Environments: Program Analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing. Language Issues: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Programming Techniques. Related Paradigms: Abductive Logic Programming, Inductive Logic Programming, Constraint Logic Programming, Answer-Set Programming. Applications: Databases, Data Integration and Federation, Software Engineering, Natural Language Processing, Web and Semantic Web, Agents, Artificial Intelligence, Bioinformatics.

Abductive logic programming agents with destructive databases

In this paper we present an agent language that combines agent functionality with a state transition theory and model-theoretic semantics. The language is based on abductive logic programming (ALP), but employs a simplified state-free syntax, with an operational semantics that uses destructive updates to manipulate a database, which represents the current state of the environment. The language builds upon the ALP combination of logic programs, to represent an agent’s beliefs, and integrity constraints, to represent the agent’s goals. Logic programs are used to define macro-actions, intensional predicates, and plans to reduce goals to sub-goals including actions. Integrity constraints are used to represent reactive rules, which are triggered by the current state of the database and recent agent actions and external events. The execution of actions and the assimilation of observations generate a sequence of database states. In the case of the successful solution of all goals, this sequence, taken as a whole, determines a model that makes the agent’s goals and beliefs all true.

Learning specifications of interaction protocols and business processes and proving their properties

In this paper we overview our recent research activity concerning the induction of Logic Programming specifications, and the proof of their properties via Abductive Logic Programming. Both the inductive and abductive tools here briefly described have been applied to respectively learn and verify (properties of) interaction protocols in multi-agent systems, Web service choreographies, careflows and business processes.