Measuring and repairing inconsistency in probabilistic knowledge bases

AbstractIn this paper we present a family of measures aimed at determining the amount of inconsistency in probabilistic knowledge bases. Our approach to measuring inconsistency is graded in the sense that we consider minimal adjustments in the degrees of certainty (i.e., probabilities in this paper) of the statements necessary to make the knowledge base consistent. The computation of the family of measures we present here, in as much as it yields an adjustment in the probability of each statement that restores consistency, provides the modeler with possible repairs of the knowledge base. The case example that motivates our work and on which we test our approach is the knowledge base of CADIAG-2, a well-known medical expert system

From Semantic Games to Provability: The Case of Gödel Logic

We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al. (in: M.-J. Lesot, S. Vieira, M.Z. Reformat, J.P. Carvalho, A. Wilbik, B. Bouchon-Meunier, and R.R. Yager, (eds.), Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted to a provability game using the concept of disjunctive strategies. Winning strategies in the provability game, with and without constants and involutive negations, turn out to correspond to analytic proofs in a version of SeqGZL (A. Ciabattoni, and T. Vetterlein, Fuzzy Sets and Systems 161(14):1941–1958, 2010) and in a sequent-of-relations calculus (M. Baaz, and Ch.G. Fermüller, in: N.V. Murray, (ed.), Automated reasoning with analytic tableaux and related methods, Springer, Berlin, 1999, pp. 36–51) respectively

Open Data

Open data is freely usable, reusable, or redistributable by anybody, provided there are safeguards in place that protect the data’s integrity and transparency. This book describes how data retrieved from public open data repositories can improve the learning qualities of digital networking, particularly performance and reliability. Chapters address such topics as knowledge extraction, Open Government Data (OGD), public dashboards, intrusion detection, and artificial intelligence in healthcare

An " expert system building tool" incorporated with fuzzy concepts.

by Lam Wai.Thesis (M.Ph.)--Chinese University of Hong Kong, 1988.Bibliography: leaves 216-220

ON SOME AXIOMATIC EXTENSIONS OF THE MONOIDAL T-NORM BASED LOGIC MTL: AN ANALYSIS IN THE PROPOSITIONAL AND IN THE FIRST-ORDER CASE

The scientific area this thesis belongs to are many-valued logics: in particular, the logic MTL and some of its extensions, in the propositional and in the first-order case (see [8],[9],[6],[7]). The thesis is divided in two parts: in the first one the necessary background about these logics, with some minor new results, are presented. The second part is devoted to more specific topics: there are five chapters, each one about a different problem. In chapter 6 a temporal semantics for Basic Logic BL is presented. In chapter 7 we move to first-order logics, by studying the supersoundness property: we have improved some previous works about this theme, by expanding the analysis to many extensions of the first-order version of MTL. Chapter 8 is dedicated to four different families of n-contractive axiomatic extensions of BL, analyzed in the propositional and in the first-order case: completeness, computational and arithmetical complexity, amalgamation and interpolation properties are studied. Finally, chapters 9 and 10 are about Nilpotent Minimum logic (NM, see [8]): in chapter 9 the sets of tautologies of some NM-chains (subalgebras of [0,1]_NM) are studied, compared and the problems of axiomatization and undecidability are tackled. Chapter 10, instead, concerns some logical and algebraic properties of (propositional) Nilpotent Minimum logic. The results (or an extended version of them) of these last chapters have been also presented in papers [1, 4, 5, 2, 3]. ---------------------------------References--------------------------------------------- [1] S. Aguzzoli, M. Bianchi, and V. Marra. A temporal semantics for Basic Logic. Studia Logica, 92(2), 147-162, 2009. doi:10.1007/s11225-009-9192-3. [2] M. Bianchi. First-order Nilpotent Minimum Logics: first steps. Submitted for publication,2010. [3] M. Bianchi. On some logical and algebraic properties of Nilpotent Minimum logic and its relation with G\uf6del logic. Submitted for publication, 2010. [4] M. Bianchi and F. Montagna. Supersound many-valued logics and Dedekind-MacNeille completions. Arch. Math. Log., 48(8), 719-736, 2009. doi:10.1007/s00153-009-0145-3. [5] M. Bianchi and F. Montagna. n-contractive BL-logics. Arch. Math. Log., 2010. doi:10.1007/s00153-010-0213-8. [6] P. Cintula, F. Esteva, J. Gispert, L. Godo, F. Montagna, and C. Noguera. Distinguished algebraic semantics for t-norm based fuzzy logics: methods and algebraic equivalencies. Ann. Pure Appl. Log., 160(1), 53-81, 2009. doi:10.1016/j.apal.2009.01.012. [7] P. Cintula and P. H\ue1jek. Triangular norm predicate fuzzy logics. Fuzzy Sets Syst., 161(3), 311-346, 2010. doi:10.1016/j.fss.2009.09.006. [8] F. Esteva and L. Godo. Monoidal t-norm based logic: Towards a logic for left-continuous t-norms. Fuzzy sets Syst., 124(3), 271-288, 2001. doi:10.1016/S0165-0114(01)00098-7. [9] P. H\ue1jek. Metamathematics of Fuzzy Logic, volume 4 of Trends in Logic. Kluwer Academic Publishers, paperback edition, 1998. ISBN:9781402003707

On some axiomatic extensions of the monoidal T-norm based logic MTL : an analysis in the propositional and in the first-order case

The scientific area this book belongs to are many-valued logics: in particular, the logic MTL and some of its extensions, in the propositional and in the first-order case. The book is divided in two parts: in the first one the necessary background about these logics, with some minor new results, are presented. The second part is devoted to more specific topics: there are five chapters, each one about a different problem. In chapter 6 a temporal semantics for Basic Logic BL is presented. In chapter 7 we move to first-order logics, by studying the supersoundness property: we have improved some previous works about this theme, by expanding the analysis to many extensions of the first-order version of MTL. Chapter 8 is dedicated to four different families of n-contractive axiomatic extensions of BL, analyzed in the propositional and in the first-order case: completeness, computational and arithmetical complexity, amalgamation and interpolation properties are studied. Finally, chapters 9 and 10 are about Nilpotent Minimum logic: in chapter 9 the sets of tautologies of some NM-chains (subalgebras of [0,1]_NM) are studied, compared and the problems of axiomatization and undecidability are tackled. Chapter 10, instead, concerns some logical and algebraic properties of (propositional) Nilpotent Minimum logic. The results (or an extended version of them) of these last chapters have been also presented in papers

Mathematics in the context of fuzzy sets: basic ideas, concepts, and some remarks on the history and recent trends of development

The main aim of this paper is to discuss the basic ideas and concepts of the so called ‘Fuzzy Mathematics’ and to give a brief survey of the history and of some trends in recent development of mathematics and its applications in the context of fuzzy sets. As a potential reader we imagine a mathematician, who is not working in the field of ‘fuzzy mathematics’, but wishes to have some idea about this vast field in modern science

Automatic production and integration of knowledge to the support of the decision and planning activities in medical-clinical diagnosis, treatment and prognosis.

El concepto de procedimiento médico se refiere al conjunto de actividades seguidas por los profesionales de la salud para solucionar o mitigar el problema de salud que afecta a un paciente. La toma de decisiones dentro del procedimiento médico ha sido, por largo tiempo, uno de las áreas más interesantes de investigación en la informática médica y el contexto de investigación de esta tesis. La motivación para desarrollar este trabajo de investigación se basa en tres aspectos fundamentales: no hay modelos de conocimiento para todas las actividades médico-clínicas que puedan ser inducidas a partir de datos médicos, no hay soluciones de aprendizaje inductivo para todas las actividades de la asistencia médica y no hay un modelo integral que formalice el concepto de procedimiento médico. Por tanto, nuestro objetivo principal es desarrollar un modelo computable basado en conocimiento que integre todas las actividades de decisión y planificación para el diagnóstico, tratamiento y pronóstico médico-clínicos. Para alcanzar el objetivo principal, en primer lugar, explicamos el problema de investigación. En segundo lugar, describimos los antecedentes del problema de investigación desde los contextos médico e informático. En tercer lugar, explicamos el desarrollo de la propuesta de investigación, basada en cuatro contribuciones principales: un nuevo modelo, basado en datos y conocimiento, para la actividad de planificación en el diagnóstico y tratamiento médico-clínicos; una novedosa metodología de aprendizaje inductivo para la actividad de planificación en el diagnóstico y tratamiento médico-clínico; una novedosa metodología de aprendizaje inductivo para la actividad de decisión en el pronóstico médico-clínico, y finalmente, un nuevo modelo computable, basado en datos y conocimiento, que integra las actividades de decisión y planificación para el diagnóstico, tratamiento y pronóstico médico-clínicos.The concept of medical procedure refers to the set of activities carried out by the health care professionals to solve or mitigate the health problems that affect a patient. Decisions making within a medical procedure has been, for a long time, one of the most interesting research areas in medical informatics and the research context of this thesis. The motivation to develop this research work is based on three main aspects: Nowadays there are not knowledge models for all the medical-clinical activities that can be induced from medical data, there are not inductive learning solutions for all the medical-clinical activities, and there is not an integral model that formalizes the concept of medical procedure. Therefore, our main objective is to develop a computable model based in knowledge that integrates all the decision and planning activities for the medical-clinical diagnosis, treatment and prognosis. To achieve this main objective: first, we explain the research problem. Second, we describe the background of the work from both the medical and the informatics contexts. Third, we explain the development of the research proposal based on four main contributions: a novel knowledge representation model, based in data, to the planning activity in medical-clinical diagnosis and treatment; a novel inductive learning methodology to the planning activity in diagnosis and medical-clinical treatment; a novel inductive learning methodology to the decision activity in medical-clinical prognosis, and finally, a novel computable model, based on data and knowledge, which integrates the decision and planning activities of medical-clinical diagnosis, treatment and prognosis