Default Logic Models of Certain Inheritance Systems with Exceptions

1993 ◽  
Vol 18 (2-4) ◽  
pp. 129-149
Author(s):  
Serge Garlatti
Keyword(s):  
Hierarchical Structure ◽  
Formal Semantics ◽  
Sufficient Conditions ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Representation Systems ◽  
The Hierarchical Structure ◽  
Necessary And Sufficient ◽  
Structure Of Knowledge ◽  
Made In

Representation systems based on inheritance networks are founded on the hierarchical structure of knowledge. Such representation is composed of a set of objects and a set of is-a links between nodes. Objects are generally defined by means of a set of properties. An inheritance mechanism enables us to share properties across the hierarchy, called an inheritance graph. It is often difficult, even impossible to define classes by means of a set of necessary and sufficient conditions. For this reason, exceptions must be allowed and they induce nonmonotonic reasoning. Many researchers have used default logic to give them formal semantics and to define sound inferences. In this paper, we propose a survey of the different models of nonmonotonic inheritance systems by means of default logic. A comparison between default theories and inheritance mechanisms is made. In conclusion, the ability of default logic to take some inheritance mechanisms into account is discussed.

scholarly journals Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 84 ◽  
Author(s):  
Sopo Pkhakadze ◽  
Hans Tompits
Keyword(s):  
Proof Theory ◽  
Consistency Condition ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Inference Process ◽  
Default Theory ◽  
Valid Inference ◽  
The One ◽  
Base Logic ◽  
Selection Of

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

Default logic and specification of nonmonotonic reasoning

2001 ◽  
Vol 13 (2) ◽  
pp. 99-112 ◽  
Author(s):  
Joeri Engelfriet ◽  
V. Wiktor Marek ◽  
Jan Treur ◽  
Miroslaw Truszczynski
Keyword(s):  
Nonmonotonic Reasoning ◽  
Default Logic

Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming

2021 ◽  
Author(s):  
Jesse Heyninck ◽  
Ofer Arieli
Keyword(s):  
Logic Programming ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Autoepistemic Logic ◽  
Algebraic Framework ◽  
Nonmonotonic Logics

Approximation fixpoint theory (AFT) constitutes an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

Infinitary default logic for specification of nonmonotonic reasoning

1996 ◽  
pp. 224-236 ◽  
Author(s):  
Joeri Engelfriet ◽  
V. Wiktor Marek ◽  
Jan Treur ◽  
Mirosław Truszczyński
Keyword(s):  
Nonmonotonic Reasoning ◽  
Default Logic

scholarly journals Reasoning about Minimal Belief and Negation as Failure

1999 ◽  
Vol 11 ◽  
pp. 277-300 ◽  
Author(s):  
R. Rosati
Keyword(s):  
Logic Programming ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Polynomial Hierarchy ◽  
Autoepistemic Logic ◽  
The Third ◽  
Negation As Failure ◽  
Negative Introspection

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.

scholarly journals Space Efficiency of Propositional Knowledge Representation Formalisms

2000 ◽  
Vol 13 ◽  
pp. 1-31 ◽  
Author(s):  
M. Cadoli ◽  
F. M. Donini ◽  
P. Liberatore ◽  
M. Schaerf
Keyword(s):  
Knowledge Representation ◽  
Belief Revision ◽  
Time Complexity ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Propositional Knowledge ◽  
Stable Model ◽  
Logic Programs ◽  
Space Efficiency ◽  
Relative Ability

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class.

A Framework for Nonmonotonic Reasoning with Rule Priorities

1998 ◽  
Vol 2 (1) ◽  
pp. 16-25
Author(s):  
Masato Shibasaki ◽  
◽  
Katsumi Nitta
Keyword(s):  
Special Form ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Logic Programs ◽  
Rule Based ◽  
Argumentation Framework ◽  
Default Rules

In the 1990, a number of studies was made on nonmonotonic reasoning with rule priorities. Little is known, however, about relationships among these semantics because there is no framework in which these semantics can be compared. In this paper, we give the basis of this framework, which is a special form of Dung’s argumentation framework, although not covering all semantics of past studies in this category. To be concrete, we provide rule-based framework (RF) for extended logic programs (ELPs), clarify semantics of default rules and rule priorities, and extend it to RF for prioritized extended default logic programs (EDLPs). By means of RF for prioritized EDLPs, we reformulate several semantics of past studies , indicate their improvements, and give new prioritized EDLPs semantics.

Sign in / Sign up

Export Citation Format

Share Document