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29
Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 610 (14 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
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
Nonmonotonic Logics and Semantics
 Journal of Logic and Computation
, 2001
"... Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas i a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may be deduced from a set A of formulas i a holds in all of th ..."
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Cited by 31 (4 self)
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Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas i a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may be deduced from a set A of formulas i a holds in all of the preferred models in which all the elements of A hold. Shoham proposed that the notion of preferred models be de ned by a partial ordering on the models of the underlying language. A more general semantics is described in this paper, based on a set of natural properties of choice functions. This semantics is here shown to be equivalent to a semantics based on comparing the relative importance of sets of models, by what amounts to a qualitative probability measure. The consequence operations de ned by the equivalent semantics are then characterized by a weakening of Tarski's properties in which the monotonicity requirement is replaced by three weaker conditions. Classical propositional connectives are characterized by natural introductionelimination rules in a nonmonotonic setting. Even in the nonmonotonic setting, one obtains classical propositional logic, thus showing that monotonicity is not required to justify classical propositional connectives.
Pragmatics and the Lexicon
 In
, 2004
"... This contribution investigates the interactions between the (mental) lexicon and pragmatics. It aims to give an overview about pragmatic phenomena that are connected with the semantic underspecification of lexical items. Cases in point are the pragmatics of adjectives, effects of negative strength ..."
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Cited by 17 (1 self)
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This contribution investigates the interactions between the (mental) lexicon and pragmatics. It aims to give an overview about pragmatic phenomena that are connected with the semantic underspecification of lexical items. Cases in point are the pragmatics of adjectives, effects of negative strengthening, systematic polysemy, the distribution of lexical and productive causatives, blocking phenomena, the interpretation of compounds, and many phenomena presently discussed within the framework of Cognitive Semantics. After emphasizing some important consequences of the traditional view of lexical semantics  the contrastive analysis of lexemes within the KatzFodor tradition of semantics , several phenomena are collected that seem to conflict with the theoretical settings made by it. These phenomena are taken as arguments in favor of a particular account of the division of labor between lexical semantics and pragmatics. This account combines the idea of (radical) semantic underspecification in the lexicon with a theory of pragmatic strengthening, based on conversational implicatures. The basic pragmatic mechanism can be expressed within the framework of (bidirectional) optimality theory for interpretation. It is suggested that this approach may provide a principled account of several of the lexicalpragmatic phenomena that are currently discussed. 1
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
Behavioral algebraization of logics
, 2008
"... Abstract. We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of manysorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL towards providing a meaningful a ..."
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Cited by 6 (6 self)
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Abstract. We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of manysorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL towards providing a meaningful algebraic counterpart also to logics with a manysorted language, and possibly including nontruthfunctional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way towards a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several wellknown characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach.
Programming interfaces and basic topology
 Annals of Pure and Applied Logic
, 2005
"... A pattern of interaction that arises again and again in programming, is a “handshake”, in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent —the client or Angel, and concluded by the other —the server or Demon. We ..."
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Cited by 6 (0 self)
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A pattern of interaction that arises again and again in programming, is a “handshake”, in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent —the client or Angel, and concluded by the other —the server or Demon. We present a category in which the objects —called interaction structures in the paper — serve as descriptions of services provided across such handshaken interfaces. The morphisms —called (general) simulations— model components that provide one such service, relying on another. The morphisms are relations between the underlying sets of the interaction structures. The proof that a relation is a simulation can serve (in principle) as an executable program, whose specification is that it provides the service described by its domain, given an implementation of the service described by its codomain.
Defining new universes in manysorted logic
 A. Rényi Institute of Mathematics
, 2001
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Transformation Methods in LDS
 In Logic, Language and Reasoning. An Essay in Honor of Dov Gabbay
, 1997
"... this paper we shall, instead, use a fragment of this family of logics as a casestudy to illustrate a set of methods originating in the LDS program. In particular, we aim to illuminate the following aspects: (I) By virtue of the extra power of labels and labelling algebras, traditional proof systems ..."
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Cited by 3 (3 self)
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this paper we shall, instead, use a fragment of this family of logics as a casestudy to illustrate a set of methods originating in the LDS program. In particular, we aim to illuminate the following aspects: (I) By virtue of the extra power of labels and labelling algebras, traditional proof systems can be transformed so as to become applicable over a much wider territory whilst retaining a uniform structure. Different logics can be obtained by defining different labelling algebras, which therefore act as "parameters", and the transition from one logic to another can be captured as a parameterchanging process which leaves the structure of deductions unchanged