Formalization of Inheritance Reasoning in Autoepistemic Logic

1990 ◽  
Vol 13 (4) ◽  
pp. 403-443
Author(s):  
Michael Gelfond ◽  
Halina Przymusinska
Keyword(s):  
General Framework ◽  
Nonmonotonic Reasoning ◽  
Commonsense Reasoning ◽  
Autoepistemic Logic

Current research in the area of nonmonotonic reasoning suggests that autoepistemic logic provides a general framework for formalizing commonsense reasoning in various domains of discourse. The goal of this paper is to investigate the suitability of autoepistemic logic for formalization of some forms of inheritance reasoning. To this end we propose a new semantics for inheritance networks with exceptions based on autoepistemic 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.

scholarly journals A General Framework for Ampliative Inference Patterns

1998 ◽  
Vol 1 (2) ◽  
Author(s):  
Claudio Delrieux
Keyword(s):  
Expert Systems ◽  
Intelligent Systems ◽  
General Framework ◽  
General Pattern ◽  
Nonmonotonic Reasoning ◽  
Reasoning Systems ◽  
Research Programmes ◽  
Complete Procedure ◽  
Information Errors ◽  
Ampliative Inference

Non trivial reasoning from contradictory premises is being acknowledged as one of the most important features in intelligent systems. Expert systems, planners and schedulers, and diagnosers, are almost always faced to potentially fallacious information, errors, uncertainty, and difference of opinions. In thesecases, we expect that the reasoning systems will not collapse. Instead, the rational expected behavior is to isolate the source of contradiction. Several systems for reasoning from contradictory premises have been advanced, usually within acontext of strict, monotonic knowledge. In this work we investigate how defeasible knowledge can be also handled in these systems. The key idea is to represent pieces of defeasible knowledge ordered within anepistemic importance relation. A semantic characterization is provided, and a sound and complete procedure to compute conclusions is also given. Then, we show how nonmonotonic reasoning and other patterns of ampliative inference like abduction and induction can be adequately recast within the general pattern of reasoning from contradiction. We discuss some applications, in particular, a brief formalization of scientific research programmes. 

A Unifying Approach for Nonmonotonic S4F, (Reflexive) Autoepistemic Logic, and Answer Set Programming

2020 ◽  
Vol 176 (3-4) ◽  
pp. 205-234
Author(s):  
Ezgi Iraz Su
Keyword(s):  
Nonmonotonic Reasoning ◽  
Answer Set Programming ◽  
General Purpose ◽  
Modal Logics ◽  
General Strategy ◽  
Autoepistemic Logic ◽  
Nonmonotonic Modal Logics ◽  
The Given ◽  
Important Form ◽  
Answer Set

This paper presents a general strategy, bringing together some major types of nonmonotonic reasoning under a monotonic bimodal setting. Such formalisms are also of interest to the fields of knowledge representation and declarative programming. We exemplify the methodology, capturing minimal model reasoning that underlies nonmonotonicity over S4F first, but then we also show how to apply the technique to other nonmonotonic logics respectively based on the modal logics KD45 and SW5. We naturally succeed it, by modifying only the axioms of the underlying modal logic and show that it successfully works. The last two formalisms are also known as autoepistemic logic (AEL) and its reflexive extension (RAEL) in the given order: AEL is an important form of nonmonotonic reasoning, introduced by Robert C. Moore in order to allow an agent to reason about his own knowledge. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, proposed more recently by David Pearce as a semantical framework for answer set programming (ASP). The latter is an efficient declarative problem solving approach with lots of applications to science and technology. Fariñas et al. have embedded EL (and so ASP) into a monotonic bimodal logic. We take this work as an initiative and successfully apply a similar methodology to closely aligned nonmonotonic modal logics. We finally discuss the potential capability to subsume the epistemic extensions of ASP within our unified paradigm.

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 A General Framework for Ampliative Inference Patterns

1998 ◽  
Vol 1 (2) ◽  
Author(s):  
Claudio Delrieux
Keyword(s):  
Expert Systems ◽  
Intelligent Systems ◽  
General Framework ◽  
General Pattern ◽  
Nonmonotonic Reasoning ◽  
Reasoning Systems ◽  
Research Programmes ◽  
Complete Procedure ◽  
Information Errors ◽  
Ampliative Inference

Non trivial reasoning from contradictory premises is being acknowledged as one of the most important features in intelligent systems. Expert systems, planners and schedulers, and diagnosers, are almost always faced to potentially fallacious information, errors, uncertainty, and difference of opinions. In thesecases, we expect that the reasoning systems will not collapse. Instead, the rational expected behavior is to isolate the source of contradiction. Several systems for reasoning from contradictory premises have been advanced, usually within acontext of strict, monotonic knowledge. In this work we investigate how defeasible knowledge can be also handled in these systems. The key idea is to represent pieces of defeasible knowledge ordered within anepistemic importance relation. A semantic characterization is provided, and a sound and complete procedure to compute conclusions is also given. Then, we show how nonmonotonic reasoning and other patterns of ampliative inference like abduction and induction can be adequately recast within the general pattern of reasoning from contradiction. We discuss some applications, in particular, a brief formalization of scientific research programmes. 

Phonologically conditioned allomorphy in the morphology of Surmiran (Rumantsch)

2008 ◽  
Vol 1 (2) ◽  
pp. 109-134 ◽  
Author(s):  
Stephen R. Anderson
Keyword(s):  
Optimality Theory ◽  
General Framework ◽  
Great Majority ◽  
Historical Change ◽  
Romance Languages ◽  
Morphological Properties ◽  
Entire System ◽  
Verbal System ◽  
Extended Sense ◽  
Phonological Rule

Alternations between allomorphs that are not directly related by phonological rule, but whose selection is governed by phonological properties of the environment, have attracted the sporadic attention of phonologists and morphologists. Such phenomena are commonly limited to rather small corners of a language's structure, however, and as a result have not been a major theoretical focus. This paper examines a set of alternations in Surmiran, a Swiss Rumantsch language, that have this character and that pervade the entire system of the language. It is shown that the alternations in question, best attested in the verbal system, are not conditioned by any coherent set of morphological properties (either straightforwardly or in the extended sense of ‘morphomes’ explored in other Romance languages by Maiden). These alternations are, however, straightforwardly aligned with the location of stress in words, and an analysis is proposed within the general framework of Optimality Theory to express this. The resulting system of phonologically conditioned allomorphy turns out to include the great majority of patterning which one might be tempted to treat as productive phonology, but which has been rendered opaque (and subsequently morphologized) as a result of the working of historical change.

More's usage of Latin verbal predicates: the particular case of fio

Moreana ◽  
2019 ◽  
Vol 56 (Number 211) (1) ◽  
pp. 97-120
Author(s):  
Concepción Cabrillana
Keyword(s):  
General Framework ◽  
Medieval Latin ◽  
Lexical Semantic ◽  
Syntactic Features ◽  
Comparative Review ◽  
Poetic Text

This article addresses Thomas More's use of an especially complex Latin predicate, fio, as a means of examining the degree of classicism in this aspect of his writing. To this end, the main lexical-semantic and syntactic features of the verb in Classical Latin are presented, and a comparative review is made of More's use of the predicate—and also its use in texts contemporaneous to More, as well as in Late and Medieval Latin—in both prose and poetry. The analysis shows that he works within a general framework of classicism, although he introduces some of his own idiosyncrasies, these essentially relating to the meaning of the verb that he employs in a preferential way and to the variety of verbal forms that occur in his poetic text.

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