Tim: The toulouse inference machine for non-classical logic programming

2005 ◽  
pp. 366-382 ◽  
Author(s):  
Philippe Balbiani ◽  
Andreas Herzig ◽  
Mamede Lima Marques
Keyword(s):  
Logic Programming ◽  
Classical Logic

scholarly journals Traditional Logic and Computational Thinking

Philosophies ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 12
Author(s):  
J.-Martín Castro-Manzano
Keyword(s):  
Logic Programming ◽  
Classical Logic ◽  
Computational Thinking ◽  
Traditional Logic ◽  
Aristotelian Logic

In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming.

scholarly journals A Transformation-based implementation for CLP with qualification and proximity

2012 ◽  
Vol 14 (1) ◽  
pp. 1-63 ◽  
Author(s):  
R. CABALLERO ◽  
M. RODRÍGUEZ-ARTALEJO ◽  
C. A. ROMERO-DÍAZ
Keyword(s):  
Information Retrieval ◽  
Logic Programming ◽  
Classical Logic ◽  
Constraint Logic Programming ◽  
Transformation Technique ◽  
Programming Paradigm ◽  
Similarity Relations ◽  
Powerful Constraint ◽  
Intended Use

AbstractUncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical logic programming paradigm. However, few of these are designed as extensions of the well-established and powerful Constraint Logic Programming (CLP) scheme for CLP. In a previous work we have proposed the proximity-based qualified constraint logic programming (SQCLP) scheme as a quite expressive extension of CLP with support for qualification values and proximity relations as generalizations of uncertainty values and similarity relations, respectively. In this paper we provide a transformation technique for transforming SQCLP programs and goals into semantically equivalent CLP programs and goals, and a practical Prolog-based implementation of some particularly useful instances of the SQCLP scheme. We also illustrate, by showing some simple – and working – examples, how the prototype can be effectively used as a tool for solving problems where qualification values and proximity relations play a key role. Intended use of SQCLP includes flexible information retrieval applications.

scholarly journals Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

2014 ◽  
Vol 14 (4-5) ◽  
pp. 725-737 ◽  
Author(s):  
ANGELOS CHARALAMBIDIS ◽  
ZOLTÁN ÉSIK ◽  
PANOS RONDOGIANNIS
Keyword(s):  
Fixed Point ◽  
Logic Programming ◽  
Classical Logic ◽  
Fixed Point Theory ◽  
Logic Program ◽  
Point Theory ◽  
Higher Order ◽  
Order Logic ◽  
New Paradigm ◽  
Higher Order Logic

AbstractExtensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique minimum infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensional higher-order logic programming. Using our approach, we resolve an old paradox that was introduced by W. W. Wadge in order to demonstrate the semantic difficulties of higher-order logic programming.

scholarly journals Forgetting an Argument

2020 ◽  
Vol 34 (03) ◽  
pp. 2750-2757
Author(s):  
Ringo Baumann ◽  
Dov Gabbay ◽  
Odinaldo Rodrigues
Keyword(s):  
Logic Programming ◽  
Classical Logic ◽  
Ad Hoc ◽  
Minimal Change ◽  
Famous Paper ◽  
Almost All

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axiomatic-driven and not limited to any specific semantics: we propose semantical and syntactical desiderata encoding different criteria for what forgetting an argument might mean; analyze how these criteria relate to each other; and check whether the criteria can be satisfied in general. The analysis is done for a number of widely used argumentation semantics. Our investigation shows that almost all desiderata are individually satisfiable. However, combinations of semantical and/or syntactical conditions reveal a much more interesting landscape. For instance, we found that the ad hoc approach to forgetting an argument, i.e., by the syntactical removal of the argument and all of its associated attacks, is too restrictive and only compatible with the two weakest semantical desiderata. Amongst the several interesting combinations identified, we showed that one satisfies a notion of minimal change and presented an algorithm that given an AF F and argument x, constructs a suitable AF G satisfying the conditions in the combination.

New method for building ASP knowledge base from knowledge in classical logic

2010 ◽  
Vol 30 (11) ◽  
pp. 2932-2936
Author(s):  
Ling-zhong ZHAO ◽  
Xue-song WANG ◽  
Jun-yan QIAN ◽  
Guo-yong CAI
Keyword(s):  
Knowledge Base ◽  
Classical Logic ◽  
New Method
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