Perception-Based Logical Deduction

In this paper, we will formalize the way, how people make inferences on the basis of the, so called, linguistic description which is a set of fuzzy IF-THEN rules understood as expressions of natural language. We will explain our idea on the following example.

[1]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[2]  Daniel Gallin,et al.  Intensional and Higher-Order Modal Logic , 1975 .

[3]  Lotfi A. Zadeh,et al.  Toward a logic of perceptions based on fuzzy logic , 2000 .

[4]  Vilém Novák,et al.  Antonyms and linguistic quantifiers in fuzzy logic , 2001, Fuzzy Sets Syst..

[5]  G. Klir,et al.  Fuzzy logic in geology , 2004 .

[6]  Peter B. Andrews.  An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[7]  Didier Dubois,et al.  Gradual inference rules in approximate reasoning , 1992, Inf. Sci..

[8]  Didier Dubois,et al.  The Semantics of Fuzzy “If … Then …” Rules , 1992 .

[9]  Vilém Novák,et al.  Formal theories and linguistic descriptions , 2004, Fuzzy Sets Syst..

[10]  Vilém Novák,et al.  From fuzzy type theory to fuzzy intensional logic , 2003, EUSFLAT Conf..

[11]  Vilém Novák,et al.  Fuzzy Approach to Reasoning and Decision-Making , 1992, Theory and Decision Library.

[12]  Vilém Novák,et al.  Linguistic If-Then Rules in Large Scale Application of Fuzzy Control , 2000 .

[13]  Vilém Novák,et al.  Fuzzy logic deduction with crisp observations , 2004, Soft Comput..

[14]  Irina Perfilieva,et al.  Normal forms for fuzzy logic functions and their approximation ability , 2001, Fuzzy Sets Syst..

[15]  V. Novák,et al.  Discovering the world with fuzzy logic , 2000 .

[16]  Vilém Novák.  Approximation abilities of perception-based logical deduction , 2003, EUSFLAT Conf..

[17]  P. Sgall,et al.  Topic-focus articulation, tripartite structures, and semantic content , 1998 .

[18]  Hashim Habiballa,et al.  The concept of LFLC 2000 - its specificity, realization and power of applications , 2003, Comput. Ind..

[19]  Lotfi A. Zadeh,et al.  Quantitative fuzzy semantics , 1971, Inf. Sci..

[20]  Pavel Materna,et al.  Concepts and objects , 1998 .

[21]  V. Novák,et al.  Mathematical Principles of Fuzzy Logic , 1999 .