A Transformation-based Implementation for CLP with Qualification and Proximity

Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme for Constraint Logic Programming. In a previous work we have proposed the SQCLP (proximity-based qualified constraint logic programming) 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.Comment: 49 pages, 5 figures, 1 table, preliminary version of an article of the same title, published as Technical Report SIC-4-10, Universidad Complutense, Departamento de Sistemas Inform\'aticos y Computaci\'on, Madrid, Spai

Incorporating the Basic Elements of a First-degree Fuzzy Logic and Certain Elments of Temporal Logic for Dynamic Management Applications

The approximate reasoning is perceived as a derivation of new formulas with the corresponding temporal attributes, within a fuzzy theory defined by the fuzzy set of special axioms. For dynamic management applications, the reasoning is evolutionary because of unexpected events which may change the state of the expert system. In this kind of situations it is necessary to elaborate certain mechanisms in order to maintain the coherence of the obtained conclusions, to figure out their degree of reliability and the time domain for which these are true. These last aspects stand as possible further directions of development at a basic logic level. The purpose of this paper is to characterise an extended fuzzy logic system with modal operators, attained by incorporating the basic elements of a first-degree fuzzy logic and certain elements of temporal logic.Dynamic Management Applications, Fuzzy Reasoning, Formalization, Time Restrictions, Modal Operators, Real-Time Expert Decision System (RTEDS)

Inconsistency Management from the Standpoint of Possibilistic Logic

International audienceUncertainty and inconsistency pervade human knowledge. Possibilistic logic, where propositional logic formulas are associated with lower bounds of a necessity measure, handles uncertainty in the setting of possibility theory. Moreover, central in standard possibilistic logic is the notion of inconsistency level of a possibilistic logic base, closely related to the notion of consistency degree of two fuzzy sets introduced by L. A. Zadeh. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, allowing for a paraconsistent form of reasoning, or associating possibilistic logic formulas with information sources or subsets of agents, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation capabilities of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic. This overview echoes the rich representation power of the possibility theory framework

Induction, complexity, and economic methodology

This paper focuses on induction, because the supposed weaknesses of that process are the main reason for favouring falsificationism, which plays an important part in scientific methodology generally; the paper is part of a wider study of economic methodology. The standard objections to, and paradoxes of, induction are reviewed, and this leads to the conclusion that the supposed ‘problem’ or ‘riddle’ of induction is a false one. It is an artefact of two assumptions: that the classic two-valued logic (CL) is appropriate for the contexts in which induction is relevant; and that it is the touchstone of rational thought. The status accorded to CL is the result of historical and cultural factors. The material we need to reason about falls into four distinct domains; these are explored in turn, while progressively relaxing the restrictions that are essential to the valid application of CL. The restrictions include the requirement for a pre-existing, independently-guaranteed classification, into which we can fit all new cases with certainty; and non-ambiguous relationships between antecedents and consequents. Natural kinds, determined by the existence of complex entities whose characteristics cannot be unbundled and altered in a piecemeal, arbitrary fashion, play an important part in the review; so also does fuzzy logic (FL). These are used to resolve two famous paradoxes about induction (the grue and raven paradoxes); and the case for believing that conventional logic is a subset of fuzzy logic is outlined. The latter disposes of all questions of justifying induction deductively. The concept of problem structure is used as the basis for a structured concept of rationality that is appropriate to all four of the domains mentioned above. The rehabilitation of induction supports an alternative definition of science: that it is the business of developing networks of contrastive, constitutive explanations of reproducible, inter-subjective (‘objective’) data. Social and psychological obstacles ensure the progress of science is slow and convoluted; however, the relativist arguments against such a project are rejected.induction; economics; methodology; complexity

Death of Paradox: The Killer Logic beneath the Standards of Proof

The prevailing but contested view of proof standards is that factfinders should determine facts by probabilistic reasoning. Given imperfect evidence, they should ask themselves what they think the chances are that the burdened party would be right if the truth were to become known; they then compare those chances to the applicable standard of proof. I contend that for understanding the standards of proof, the modern versions of logic — in particular, fuzzy logic and belief functions — work better than classical probability. This modern logic suggests that factfinders view evidence of an imprecisely perceived and described reality to form a fuzzy degree of belief in a fact’s existence; they then apply the standard of proof in accordance with the theory of belief functions, by comparing their belief in a fact’s existence to their belief in its negation. This understanding explains how the standard of proof actually works in the law world. It gives a superior mental image of the factfinders’ task, conforms more closely to what we know of people’s cognition, and captures better what the law says its standards are and how it manipulates them. One virtue of this conceptualization is that it is not a radically new view. Another virtue is that it nevertheless manages to resolve some stubborn problems of proof, including the infamous conjunction paradox