Nonground Abductive Logic Programming with Probabilistic Integrity Constraints

Abstract Uncertain 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.

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Dischargeable Obligations in the 𝒮CIFF Framework

Fundamenta Informaticae ◽

10.3233/fi-2020-1976 ◽

2020 ◽

Vol 176 (3-4) ◽

pp. 321-348

Author(s):

Marco Alberti ◽

Marco Gavanelli ◽

Evelina Lamma ◽

Fabrizio Riguzzi ◽

Ken Satoh ◽

...

Keyword(s):

Logic Programming ◽

Operational Semantics ◽

Civil Code ◽

Normative Reasoning ◽

Abductive Logic ◽

Abductive Logic Programming ◽

New Knowledge ◽

Proof Procedure ◽

Suitable 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).

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The CIFF Proof Procedure for Abductive Logic Programming with Constraints

Logics in Artificial Intelligence - Lecture Notes in Computer Science ◽

10.1007/978-3-540-30227-8_6 ◽

2004 ◽

pp. 31-43 ◽

Cited By ~ 22

Author(s):

U. Endriss ◽

P. Mancarella ◽

F. Sadri ◽

G. Terreni ◽

F. Toni

Keyword(s):

Logic Programming ◽

Abductive Logic ◽

Abductive Logic Programming ◽

Proof Procedure

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The CIFF proof procedure for abductive logic programming with constraints: Theory, implementation and experiments

Theory and Practice of Logic Programming ◽

10.1017/s1471068409990093 ◽

2009 ◽

Vol 9 (6) ◽

pp. 691-750 ◽

Cited By ~ 11

Author(s):

PAOLO MANCARELLA ◽

GIACOMO TERRENI ◽

FARIBA SADRI ◽

FRANCESCA TONI ◽

ULLE ENDRISS

Keyword(s):

Logic Programming ◽

State Of The Art ◽

Constraint Logic Programming ◽

Constraint Solver ◽

Abductive Logic ◽

Abductive Logic Programming ◽

Proof Procedure ◽

Answer Set

AbstractWe present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state-of-the-art abductive systems and answer set solvers and showing how to use it to program some applications.

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A Measure of Arbitrariness in Abductive Explanations

Theory and Practice of Logic Programming ◽

10.1017/s1471068414000271 ◽

2014 ◽

Vol 14 (4-5) ◽

pp. 665-679 ◽

Cited By ~ 1

Author(s):

LUCIANO CAROPRESE ◽

IRINA TRUBITSYNA ◽

Mirosław Truszczyński ◽

Ester Zumpano

Keyword(s):

Logic Programming ◽

Integrity Constraints ◽

Basic Properties ◽

Abductive Logic ◽

Abductive Logic Programming ◽

Detailed Picture

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.

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