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A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 77 (5 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
On rational weak nilpotent minimum logics
 J. of Mult.Valued Logic & Soft Computing
"... In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truthvalues as truth constants in the language and by adding corresponding bookkeeping axioms for the truthconstants. We also investigate the rational extensions of some parametric families of Weak ..."
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Cited by 17 (14 self)
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In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truthvalues as truth constants in the language and by adding corresponding bookkeeping axioms for the truthconstants. We also investigate the rational extensions of some parametric families of Weak Nilpotent Minimum logics, weaker than both Gödel and Nilpotent Minimum logics. Weak and strong standard completeness of these logics are studied in general and in particular when we restrict ourselves to formulas of the kind r → ϕ, where r is a rational in [0, 1] and ϕ is a formula without rational truthconstants.
Mathematical fuzzy logic as a tool for the treatment of vague information
 Information Sciences
, 2005
"... The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by ..."
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Cited by 15 (1 self)
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The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by a calculus for the derivation of formulas. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon these theoretical considerations. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1
On expansions of tnorm based logics with truthconstants, To appear
 in the book Fuzzy Logics and Related Structures
, 2007
"... This paper focuses on completeness results about generic expansions of logics of both continuous tnorms and Weak Nilpotent Minimum (WNM) with truthconstants. Indeed, we consider algebraic semantics for expansions of these logics with a set of truthconstants {r  r ∈ C}, for a suitable countable C ..."
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Cited by 13 (10 self)
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This paper focuses on completeness results about generic expansions of logics of both continuous tnorms and Weak Nilpotent Minimum (WNM) with truthconstants. Indeed, we consider algebraic semantics for expansions of these logics with a set of truthconstants {r  r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) either the tnorm is a finite ordinal sum of Lukasiewicz, Gödel and Product components (and hence continuous) or the tnorm is a Weak Nilpotent Minimum with a finite partition and (ii) the set of truthconstants covers all the unit interval in the sense that each component (in case of continuous tnorm) or each interval of the partition (in the WNM case) contains values of C in its interior. Results on expansions of the logic of a continuous tnorm were already published, while many of the results about WNM are presented here for the first time.
On product logic with truthconstants
 Journal of Logic and Computation
"... Product Logic Π is an axiomatic extension of Hájek’s Basic Fuzzy Logic BL coping with the 1tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by ad ..."
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Cited by 10 (10 self)
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Product Logic Π is an axiomatic extension of Hájek’s Basic Fuzzy Logic BL coping with the 1tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truthconstants (one truthconstant r for each r in a countable Πsubalgebra C of [0, 1]) and by adding the corresponding bookkeeping axioms for the truthconstants. We first show that the corresponding logics Π(C) are algebraizable, and hence complete with respect to the variety of Π(C)algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of Π(C) are exactly the 1tautologies of the algebra defined over the real unit interval where the truthconstants are interpreted as their own values. It is also shown that they do not enjoy the canonical strong standard completeness, but they enjoy it for finite theories when restricted to evaluated Πformulas of the kind r → ϕ, where r is a truthconstant and ϕ a formula not containing truthconstants. Finally we consider the logics Π∆(C), the expansion of Π(C) with the wellknown Baaz’s projection connective ∆, and we show canonical finite strong standard completeness for them.
The SDA* Model: A Set Theory Approach
 in 20th IEEE Int Symp on ComputerBased Medical Systems, CBMS 2007
, 2007
"... Procedural knowledge in medicine is embedded in Clinical Practice Guidelines whose textual condition makes it difficult to share and to reuse. Several languages for formal definition of clinical practice guidelines have been proposed to overcome these difficulties. In order to deal with the huge amo ..."
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Cited by 3 (1 self)
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Procedural knowledge in medicine is embedded in Clinical Practice Guidelines whose textual condition makes it difficult to share and to reuse. Several languages for formal definition of clinical practice guidelines have been proposed to overcome these difficulties. In order to deal with the huge amount of medical situations, these languages use to be extensive and complex in such a way that they, and the knowledge they are used to represent, are arduous to understand and to manage by nontrained general practitioners. The SDA * model is introduced as an alternative language that promotes representation capability and simplicity in such a way that not only computers, but also health care professionals are able to understand and manage easily without any sort of training. Here, a description of this model from a set theory perspective is provided.
Coherent Functions in Autonomous Systems
, 2002
"... INTRODUCTION Advanced sensorimotor devices, like mobile robots, are often referred to as autonomous systems. The expression is used to intentionally remark on the difference between these systems and those of traditional industrial automation. Although no rigorous definition is easily available, a ..."
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INTRODUCTION Advanced sensorimotor devices, like mobile robots, are often referred to as autonomous systems. The expression is used to intentionally remark on the difference between these systems and those of traditional industrial automation. Although no rigorous definition is easily available, a general informal consensus seems to exist on the features that denote autonomy: a system is considered the more autonomous the more reliably it can survive and perform tasks in the real world, without the need for human intervention. 171 ____________________________ *email: claudio.sossai@isib.cnr.it J. of Mult.Valued Logic & Soft Computing., Vol. 9, pp. 171194 2003 Old City Publishing, Inc. Reprints available directly from the publisher Published by license under the OCP Science imprint, Photocopying permitted by license only a member of the Old City Publishing Group In the literature different ideas and techniques have been proposed and investigated to achieve these results, nonethe
On Revising Fuzzy Belief Bases
, 2003
"... We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revisioninput formulas can come attached with varying truthdegrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncer ..."
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Cited by 3 (0 self)
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We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revisioninput formulas can come attached with varying truthdegrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truthfunctional fuzzy logics, we show how the idea of rational change from "crisp" base revision, as embodied by the idea of partial meet (base) revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy base revision and illustrate how the operation works in several important special instances of the framework.
Nonmonotonic Inference Operators for Fuzzy Logic
 IN: PROC. 9TH INTERNAT. WORKSHOP ON NONMONOTONIC REASONING, NMR’2002
, 2002
"... Fuzzy logic in an abstract sense allows to draw (graded) conclusions from only partially "given" premises i.e. fuzzy sets of formulas. This means ..."
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Cited by 3 (0 self)
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Fuzzy logic in an abstract sense allows to draw (graded) conclusions from only partially "given" premises i.e. fuzzy sets of formulas. This means
Fuzzy control as a fuzzy deduction system
, 2001
"... An approach to fuzzy control based on fuzzy logic in narrow sense (fuzzy inference rules + fuzzy set of logical axioms) is proposed. This gives an interesting theoretical framework and suggests new tools for fuzzy control. ..."
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Cited by 3 (1 self)
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An approach to fuzzy control based on fuzzy logic in narrow sense (fuzzy inference rules + fuzzy set of logical axioms) is proposed. This gives an interesting theoretical framework and suggests new tools for fuzzy control.