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Fuzzy logic as a methodology for the treatment of vagueness
 The Logica Yearbook 2004
, 2005
"... Fuzzy logic is now one of the leading and most successful methodologies for the treatment of the vagueness phenomenon. It is a wellestablished sound formal system with numerous applications. In recent years, several significant books have been published where fuzzy logic is investigated deeply and ..."
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Fuzzy logic is now one of the leading and most successful methodologies for the treatment of the vagueness phenomenon. It is a wellestablished sound formal system with numerous applications. In recent years, several significant books have been published where fuzzy logic is investigated deeply and so, its
Mathematical fuzzy control. A survey of some recent results (submitted
"... The core point of fuzzy control approaches are finite lists of linguistic control rules. For computerbased automatic control these lists have to be transformed into control algorithms which can be realized on a computer. The main general idea of this fuzzy control approach is that such an algorithm ..."
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The core point of fuzzy control approaches are finite lists of linguistic control rules. For computerbased automatic control these lists have to be transformed into control algorithms which can be realized on a computer. The main general idea of this fuzzy control approach is that such an algorithm should yield a fuzzy subset of the output space of the control problem if confronted with a fuzzy subset of the input space. This paper surveys mathematical problems which are connected with, and arose out of these basic ideas. The main formal tools used in these mathematical considerations are fuzzy sets and fuzzy relations together with some generalized, viz. manyvalued logic which underlies these considerations. And the essential way of understanding the mathematical context of fuzzy control is to look at it as an interpolation problem: one has to determine a fuzzy control function out of a finite list of interpolation nodes.
Toward problems for mathematical fuzzy logic, in
 Proc. of IEEE International Conference on Fuzzy Systems
, 2006
"... The paper discusses some open problems in the field of mathematical fuzzy logic which may have a decisive influence for the future development of fuzzy logic within the next decade. 1 ..."
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The paper discusses some open problems in the field of mathematical fuzzy logic which may have a decisive influence for the future development of fuzzy logic within the next decade. 1
What Is “The ” Fuzzy Logic ∗
"... This paper is a contribution to the discussion about the problem, whether is there a fuzzy logic that can be considered as “The ” fuzzy logic, i.e. only one formal system of fuzzy logic that would fit all our requirements and could serve ..."
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This paper is a contribution to the discussion about the problem, whether is there a fuzzy logic that can be considered as “The ” fuzzy logic, i.e. only one formal system of fuzzy logic that would fit all our requirements and could serve
SupraLogic: Using Transfinite Type Theory with Type Variables for Paraconsistency
"... Abstract. We define the paraconsistent supralogic Pσ by a typeshift from the booleans o of propositional logic Po to the suprabooleans σ of the propositional type logic P obtained as the propositional fragment of the transfinite type theory Q defined by Peter Andrews (NorthHolland Studies in Log ..."
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Abstract. We define the paraconsistent supralogic Pσ by a typeshift from the booleans o of propositional logic Po to the suprabooleans σ of the propositional type logic P obtained as the propositional fragment of the transfinite type theory Q defined by Peter Andrews (NorthHolland Studies in Logic 1965) as a classical foundation of mathematics. The supralogic is in a sense a propositional logic only, but since there is an infinite number of suprabooleans and arithmetical operations are available for this and other types, virtually anything can be specified. The supralogic is a generalization of ̷Lukasiewicz’s threevalued logic, with the intermediate value duplicated many times and ordered such that none of the copies of this value imply other ones, but it differs from ̷Lukasiewicz’s manyvalued logics as well as from logics based on bilattices (the latter have additional designated truth values). There are several automated theorem provers for classical higher order logic and it should be possible to modify these to our needs.
The Vagueness of Robot Emotions
"... As the field of robotics matures, robots will need some method of displaying and modeling emotions. One way of doing this is to use a humanlike face on which the robot can make facial expressions that correspond to its internal emotional state. Yet the connection between a robot’s emotional state a ..."
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As the field of robotics matures, robots will need some method of displaying and modeling emotions. One way of doing this is to use a humanlike face on which the robot can make facial expressions that correspond to its internal emotional state. Yet the connection between a robot’s emotional state and its physical facial expression is not an obvious one; in particular, there is no principled method of mapping changes in emotional states to changes in facial expressions. We give a philosophical analysis of the problem and show that it is rooted in the vagueness of robot emotions. We then outline several methods that have been used in the philosophical literature to model vagueness and propose an experiment that uses our humanoid robot head to determine which philosophical theory is best suited to the task.
Lukasiewicz and Modal Logic
"... . / Lukasiewicz's fourvalued modal logic is surveyed and analyzed. 1 Introduction The Polish philosopher and logician Jan / Lukasiewicz (Lw'ow, 1878  Dublin, 1956) is one of the fathers of modern manyvalued logic, and some of the systems he introduced are presently a topic of deep investigatio ..."
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. / Lukasiewicz's fourvalued modal logic is surveyed and analyzed. 1 Introduction The Polish philosopher and logician Jan / Lukasiewicz (Lw'ow, 1878  Dublin, 1956) is one of the fathers of modern manyvalued logic, and some of the systems he introduced are presently a topic of deep investigation. In particular his infinitelyvalued logic belongs to the core systems of mathematical fuzzy logic as a logic of comparative truth, cf. [3, 6, 7]. It is interesting to recall that modal notions were present in / Lukasiewicz's motivation from the start. His 1930 paper [13] on manyvalued logics is almost entirely devoted to modal propositions, and in it he says: The threevalued system of propositional logic owes its origin to certain enquiries I made into socalled "modal propositions" and the notions of possibility and necessity closely connected with them. (Quoted from [17], p. 153) And, as he tells in the preface to the second edition [16] of his book on Aristotle, it was his aim o...
Mathematical Properties of Manyvalued Logics  Thesis Proposal
, 2003
"... This thesis proposal is concerned with propositional fuzzy logics. At the beginning we give a survey of Rfuzzy logics which are based on a continuous tnorm and its residuum. Then our results in this area are presented. Firstly we define a validation set of a formula in a fuzzy logic as the set ..."
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This thesis proposal is concerned with propositional fuzzy logics. At the beginning we give a survey of Rfuzzy logics which are based on a continuous tnorm and its residuum. Then our results in this area are presented. Firstly we define a validation set of a formula in a fuzzy logic as the set of all truth values which this formula may achieve. Then we summarize characterizations of validation sets in Rfuzzy logics. Secondly we introduce PL logic which is an extension of Lukasiewicz Rfuzzy logic by the product connective. Finally we discuss possible directions of future work on the thesis.
POINCARÉ PARADOX AND APPROXIMATE SIMILARITIES by
"... This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive noti ..."
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This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive notion of “approximate similarity ” cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools to face the question with. Indeed a first order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the pointfree metric spaces is also established.
Based
"... Ordinal sums of tnorms on bounded lattices are discussed. It is shown that this construction leads always to a tnorm in the case of horizontal sums of chains. Moreover, we obtain a tnorm also if the underlying lattice is an ordinal sum (in the sense of Birkhoff) of the carriers of the summands. ..."
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Ordinal sums of tnorms on bounded lattices are discussed. It is shown that this construction leads always to a tnorm in the case of horizontal sums of chains. Moreover, we obtain a tnorm also if the underlying lattice is an ordinal sum (in the sense of Birkhoff) of the carriers of the summands.