Comparison of Energy Management Strategies between Fuzzy Logic and Mixed-Integer Linear Programming for a Hybrid Photovoltaic–Wind Powered Reverse Osmosis Desalination System

This paper includes the main notions associated with the syntax and semantics of two interesting paradigms in fuzzy logic programming with default negation: multi-adjoint normal logic programming introduced in [5] and the fuzzy answer set logic programming approach presented in [16]. We will show that fuzzy answer set logic programs can be translated into multi-adjoint normal logic programs, as long as the implication operator used in the former is a residuated implication. Moreover, we will relate the notions of fuzzy y-model and model by means of a characterization theorem which allow us to guarantee the existence of fuzzy y-models of fuzzy answer set logic programs.

Description logic programs under probabilistic uncertainty and fuzzy vagueness

This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web.More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified nonmonotonic negation), and probabilistic uncertainty in a uniform framework for the Semantic Web. We define important concepts dealing with both probabilistic uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic web applications. In the extended report, we also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity.

The new direction of the research in the field of data mining is the development of methods to handle imperfection (uncertainty, vagueness, imprecision,...). The main interest in this research is focused on probability models. Besides these there is an extensive study of the phenomena of imperfection in fuzzy logic. In this paper we concentrate especially on fuzzy logic programs (FLP) and Generalized Annotated Programs (GAP). The lack of the present research in the field of fuzzy inductive logic programming (FILP) is that every approach has its own formulation of the proof-theoretic part (often dealing with linguistic hedges) and lack sound and compete formulation of semantics. Our aim in this paper is to propose a formal model of FILP and induction of GAP programs (IGAP) based on sound and complete model of FLP (without linguistic hedges) and its equivalence with GAP. We focus on learning from entailment setting in this paper. We describe our approach to IGAP and show its consistency and equivalence to FILP. Our inductive method is used for detection of user preferences in a web search application. Finally, we compare our approach to several fuzzy ILP approaches.KeywordsLogic ProgramLogic ProgrammingInductive Logic ProgrammingDeductive PartInductive Logic Programming SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtáš, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., VeryTrue, VeryProbablyTrue and LittleFalse, taken from a hedge algebra of a linguistic truth variable, and linguistic hedges (modifiers) can be used as unary connectives in formulae. This is motivated by the fact that humans reason mostly in terms of linguistic terms rather than in terms of numbers, and linguistic hedges are often used in natural languages to express different levels of emphasis. The paper presents: (a) the language of fuzzy linguistic logic programming; (b) a declarative semantics in terms of Herbrand interpretations and models; (c) a procedural semantics which directly manipulates linguistic terms to compute a lower bound to the truth value of a query, and proves its soundness; (d) a fixpoint semantics of logic programs, and based on it, proves the completeness of the procedural semantics; (e) several applications of fuzzy linguistic logic programming; and (f) an idea of implementing a system to execute fuzzy linguistic logic programs.

A comparison of fuzzy and annotated logic programming

This paper presents fuzzy conceptual graph programs (FCGPs) as a fuzzy order-sorted logic programming system based on the structure of conceptual graphs and the approximate reasoning methodology of fuzzy logic. On one hand, it refines and completes a currently developed FCGP system that extends CGPs to deal with the pervasive vagueness and imprecision reflected in natural languages of the real world. On the other hand, it overcomes the previous wide-sense fuzzy logic programming systems to deal with uncertainty about types of objects. FCGs are reformulated with the introduction of fuzzy concept and relation types. The syntax of FCGPs based on the new formulation of FCGs and their general declarative semantics based on the notion of ideal FCGs are defined. Then, an SLD-style proof procedure for FCGPs is developed and proved to be sound and complete with respect to their declarative semantics. The procedure selects reductants rather than clauses of an FCGP in resolution steps and involves lattice-based constraint solving, which supports more expressive queries than the previous FCGP proof procedure did. The results could also be applied to CGPs as special FCGPs and useful for extensions adding to CGs lattice-based annotations to enhance their knowledge representation and reasoning power.KeywordsFuzzy LogicLogic ProgramLinguistic LabelConceptual GraphConcept NodeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Fuzzy linguistic logic programming, which is a result of integrating hedge algebras and fuzzy logic programming, is proposed to facilitate the representation and reasoning on knowledge expressed in natural language, in which vague sentences are usually given a degree of truth stated in linguistic terms rather than a number, and linguistic hedges are very often used. To compute the truth value of a query, a computational model which directly manipulates linguistic terms is provided. The computational model has been proved to be sound. This paper presents a fixpoint semantics for fuzzy linguistic logic programs and based on it proves the completeness of the computational model.

The Semantic Web is an extension of the current World Wide Web, and aims to help computers to understand and process web information automatically. In recent years, the integration ontologies and rules has become a central topic in the Semantic Web. Therefore, significant research efforts have focused on integration description logic programs. However, description logic programs cannot well model a great deal of real-world problems because of the restriction of represented formalism. To address this problem, we further extend description logic programs such that they can deal with imprecise information, uncertain information and non monotonie reasoning at the same time. In this paper, we propose tightly coupled fuzzy rough description logic programs (or simply fuzzy rough dl-program) under the answer set semantics, which are tightly integrates fuzzy rough disjunctive programs under the answer set semantics with fuzzy rough description logics. To our knowledge, this is the first such approach. First of all, we define the syntax and semantics of fuzzy rough disjunctive logic programs, which is the rough extension of fuzzy disjunctive logic programs based on rough set theory. Then, we define the syntax and semantics of fuzzy rough dl-program. Finally, we show some semantic properties of fuzzy rough dl-program under the answer set semantics.

Natural language is a principal and important means of human communication. It is used to express information as inputs to be processed by human brains then, very often, outputs are also expressed in natural language. The capacity for humans to communicate using language allows us to give, receive, and understand information expressed within a rich and flexible representational framework. Moreover, we can reason based on natural language expressions, and make decisions based on the information they convey, though this information usually involves imprecise terms and uncertain facts. How humans process information represented in natural language is still a challenge to science, in general, and to Artificial Intelligence, in particular. However, it is clear that, for a computer with the conventional processing paradigm to handle natural language, a formalism is required. For reasoning, it is desirable that such a formalism be a logical one. A logic for handling natural language should have not only a structure of formulas close to that of natural language sentences, but also a capability to deal with the semantics of vague linguistic terms pervasive in natural language expressions. Conceptual graphs (Sowa [2,3]) and fuzzy logic (Zadeh [7,8]) are two logical formalisms that emphasize the target of natural language, each of which is focused on one of the two mentioned desired features of a logic for handling natural language. While a smooth mapping between logic and natural language has been regarded as the main motivation of conceptual graphs (Sowa [4,5,6]), a methodology for computing with words has been regarded as the main contribution of fuzzy logic (Zadeh [9,10,11]). However, although conceptual graphs and fuzzy logic have the common target of natural language, until recently they were studied and developed quite separately. Their combination would be a great advantage towards a knowledge representation language that can approach the structure and expressiveness of natural language. At this juncture, conceptual graphs provide a syntactic structure for a smooth mapping to and from natural language, while fuzzy logic provides a semantic processor for approximate reasoning with words having vague meanings. This talk presents the combined result of an interdisciplinary research programme focused on the integration of conceptual graphs and fuzzy logic, towards a knowledge representation language that is close to natural language in both of the structure and expressiveness (Cao [1]). First, the talk summarizes the development of fuzzy conceptual graphs and their logic programming foundations, as a graph-based order-sorted fuzzy set logic programming language for automated reasoning with fuzzy object attributes and types. Second, it presents the extension of fuzzy conceptual graphs with general quantifiers and direct reasoning operations on these extended conceptual graphs, which could be mapped to and from generally quantified natural language statements. Third, it introduces recent applications of fuzzy conceptual graphs for understanding natural language queries and semantic search.

Thresholded Tabulation in a Fuzzy Logic Setting

Fuzzy Logic Programming is an interesting and still growing research area that agglutinates the efforts for introducing fuzzy logic into logic programming (LP), in order to incorporate more expressive resources on such languages for dealing with uncertainty and approximated reasoning. The multi‐adjoint logic programming approach is a recent and extremely flexible fuzzy logic paradigm for which, unfortunately, we have not found practical tools implemented so far. In this work, we describe a prototype system which is able to directly translate fuzzy logic programs into Prolog code in order to safely execute these residual programs inside any standard Prolog interpreter in a completely transparent way for the final user. We think that the development of such fuzzy languages and programing tools might play an important role in the design of advanced software applications for computational physics, chemistry, mathematics, medicine, industrial control and so on.

This paper presents fuzzy linguistic logic programming which is developed based on fuzzy logic programming introduced by P. Vojtas in order to facilitate the representation and reasoning on knowledge expressed in natural language. In fuzzy linguistic logic programming, truth values are linguistic terms such as true, very true, more or less true,and falsetaken from a hedge algebra of the truth variable, and linguistic hedges, e.g., very, more or less, quite,and rather, which are frequently used in natural language, can be used as unary connectives in formulae. In order to compute the truth value of a query, we provide a computational model which directly manipulates linguistic terms. The soundness of the computational model is proved. A fixpoint semantics of logic programs and the completeness of the computational model are discussed.

Tabulation proof procedures for fuzzy linguistic logic programming

We present a novel approach to fuzzy description logic programs (or simply fuzzy dl-programs) under the answer set semantics, which is a tight integration of fuzzy disjunctive logic programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly coupled disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. We show that the new formalism faithfully extends both fuzzy disjunctive logic programs and fuzzy description logics, and that under suitable assumptions, reasoning in the new formalism is decidable. We present a polynomial reduction of certain fuzzy dl-programs to tightly coupled disjunctive dl-programs, and we analyze the complexity of consistency checking and query processing for certain fuzzy dl-programs. Furthermore, we provide a special case of fuzzy dl-programs for which deciding consistency and query processing can both be done in polynomial time in the data complexity.