The Experts below are selected from a list of 16458 Experts worldwide ranked by ideXlab platform
Petr Hájek - One of the best experts on this subject based on the ideXlab platform.
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On arithmetic in the Cantor- Łukasiewicz fuzzy set theory
Archive for Mathematical Logic, 2005Co-Authors: Petr HájekAbstract:Axiomatic set theory with full comprehension is known to be consistent in Łukasiewicz fuzzy Predicate Logic. But we cannot assume the existence of natural numbers satisfying a simple schema of induction; this extension is shown to be inconsistent.
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Fuzzy Logic and Arithmetical Hierarchy III
Studia Logica, 2001Co-Authors: Petr HájekAbstract:Fuzzy Logic is understood as a Logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy Predicate Logic is determined or at least estimated.
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embedding Logics into product Logic
Studia Logica, 1998Co-Authors: Matthias Baaz, Petr Hájek, David Švejda, Jan KrajíčekAbstract:We construct a faithful interpretation of Łukasiewicz's Logic in product Logic (both propositional and Predicate). Using known facts it follows that the product Predicate Logic is not recursively axiomatizable.
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Fuzzy Logic and arithmetical hierarchy
Fuzzy Sets and Systems, 1995Co-Authors: Petr HájekAbstract:Fuzzy Logic is understood as a Logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy Predicate Logic is determined or at least estimated.
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Embedding Logics Into Product Logic
2024Co-Authors: Matthias Baaz, Petr Hájek, Jan Krajíček, David ŠvejdaAbstract:We construct a faithful interpretation of / Lukasiewicz's Logic in the product Logic (both propositional and Predicate). Using known facts it follows that the product Predicate Logic is not recursively axiomatizable. We prove a completeness theorem for the product Logic extended by a unary connective 4 of Baaz [1]. We show that Godel's Logic is a subLogic of this extended product Logic. We also prove NP-completeness of the set of propositional formulas satisfiable in product Logic (resp. in Godel's Logic). 1 Introduction We shall be concerned with many-valued Logics in this paper; in particular, in / Lukasiewicz's Logic / L, Godel's Logic G and product Logic P. Our aim is to obtain information about complexity of these Logics in terms of recursive theory (in the case of Predicate Logic) or in terms of computational complexity theory (in the case of propositional Logic). Scarpellini [13] and Mundici [9] provide such information for / Lukasiewicz's Logic. Hence we shall concentrate on ..
Usman Qamar - One of the best experts on this subject based on the ideXlab platform.
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developing an expert system based on association rules and Predicate Logic for earthquake prediction
Knowledge Based Systems, 2015Co-Authors: Aqdas Ikram, Usman QamarAbstract:Expert systems (ES) are a branch of applied artificial intelligence. The basic idea behind ES is simply that expertise, which is the vast body of task-specific knowledge, is transferred from a human to a computer. ES provide powerful and flexible means for obtaining solutions to a variety of problems that often cannot be dealt with by other, more traditional and orthodox methods. Thus, their use is proliferating to many sectors of our social and technoLogical life, where their applications are proving to be critical in the process of decision support and problem solving. Earthquake professionals for many decades have recognized the benefits to society from reliable earthquake predictions, but uncertainties regarding source initiation, rupture phenomena, and accuracy of both the timing and magnitude of the earthquake occurrence have often times seemed either very difficult or impossible to overcome. This research proposes and implements an expert system to predict earthquakes from previous data. This is achieved by applying association rule mining on earthquake data from 1972 to 2013. These associations are polished using Predicate-Logic techniques to draw stimulating production-rules to be used with a rule-based expert system. The proposed expert system was able to predict all earthquakes which actually occurred within 12h at-most.
Larry S Davis - One of the best experts on this subject based on the ideXlab platform.
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Predicate Logic based image grammars for complex pattern recognition
International Journal of Computer Vision, 2011Co-Authors: Vinay Shet, Maneesh Singh, Claus Bahlmann, Visvanathan Ramesh, Jan Neumann, Larry S DavisAbstract:Predicate Logic based reasoning approaches provide a means of formally specifying domain knowledge and manipulating symbolic information to explicitly reason about different concepts of interest. Extension of traditional binary Predicate Logics with the bilattice formalism permits the handling of uncertainty in reasoning, thereby facilitating their application to computer vision problems. In this paper, we propose using first order Predicate Logics, extended with a bilattice based uncertainty handling formalism, as a means of formally encoding pattern grammars, to parse a set of image features, and detect the presence of different patterns of interest. Detections from low level feature detectors are treated as Logical facts and, in conjunction with Logical rules, used to drive the reasoning. Positive and negative information from different sources, as well as uncertainties from detections, are integrated within the bilattice framework. We show that this approach can also generate proofs or justifications (in the form of parse trees) for each hypothesis it proposes thus permitting direct analysis of the final solution in linguistic form. Automated Logical rule weight learning is an important aspect of the application of such systems in the computer vision domain. We propose a rule weight optimization method which casts the instantiated inference tree as a knowledge-based neural network, interprets rule uncertainties as link weights in the network, and applies a constrained, back-propagation algorithm to converge upon a set of rule weights that give optimal performance within the bilattice framework. Finally, we evaluate the proposed Predicate Logic based pattern grammar formulation via application to the problems of (a) detecting the presence of humans under partial occlusions and (b) detecting large complex man made structures as viewed in satellite imagery. We also evaluate the optimization approach on real as well as simulated data and show favorable results.
Frank M Brown - One of the best experts on this subject based on the ideXlab platform.
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decision procedures for the propositional cases of second order Logic and z modal Logic representations of a first order l Predicate nonmonotonic Logic
Lecture Notes in Computer Science, 2003Co-Authors: Frank M BrownAbstract:Decision procedures for the propositional cases of two different Logical representations for an L-Predicate Logic generalizing Autoepistemic Logic to handle quantified variables over modal scopes are described. The first representation is Second Order Logic. The second is Z Modal Logic which extends its S5 modal laws with laws stating what is Logically possible. It is suggested that certain problems are more easily solved using one representation whereas other problems are more easily solved using the other.
Sam Staton - One of the best experts on this subject based on the ideXlab platform.
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an algebraic presentation of Predicate Logic
Foundations of Software Science and Computation Structure, 2013Co-Authors: Sam StatonAbstract:We present an algebraic theory for a fragment of Predicate Logic. The fragment has disjunction, existential quantification and equality. It is not an algebraic theory in the classical sense, but rather within a new framework that we call 'parameterized algebraic theories'. We demonstrate the relevance of this algebraic presentation to computer science by identifying a programming language in which every type carries a model of the algebraic theory. The result is a simple functional Logic programming language. We provide a syntax-free representation theorem which places terms in bijection with sieves, a concept from category theory. We study presentation-invariance for general parameterized algebraic theories by providing a theory of clones. We show that parameterized algebraic theories characterize a class of enriched monads.
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an algebraic presentation of Predicate Logic extended abstract
Foundations of Software Science and Computation Structure, 2013Co-Authors: Sam StatonAbstract:We present an algebraic theory for a fragment of Predicate Logic. The fragment has disjunction, existential quantification and equal- ity. It is not an algebraic theory in the classical sense, but rather within a new framework that we call 'parameterized algebraic theories'. We demonstrate the relevance of this algebraic presentation to com- puter science by identifying a programming language in which every type carries a model of the algebraic theory. The result is a simple functional Logic programming language. We provide a syntax-free representation theorem which places terms in bijection with sieves, a concept from category theory. We study presentation-invariance for general parameterized algebraic theories by providing a theory of clones. We show that parameterized algebraic theories characterize a class of enriched monads.
