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Deduction in ManyValued Logics: a Survey
 Mathware & Soft Computing, iv(2):6997
, 1997
"... this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of man ..."
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this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of manyvalued logics according to their intended application
A Resolution Calculus for Presuppositions
 Proceedings of the 12th ECAI
, 1996
"... . The semantics of everyday language and the semantics of its naive translation into classical firstorder language considerably differ. An important discrepancy that is addressed in this paper is about the implicit assumption what exists. For instance, in the case of universal quantification natura ..."
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. The semantics of everyday language and the semantics of its naive translation into classical firstorder language considerably differ. An important discrepancy that is addressed in this paper is about the implicit assumption what exists. For instance, in the case of universal quantification natural language uses restrictions and presupposes that these restrictions are nonempty, while in classical logic it is only assumed that the whole universe is nonempty. On the other hand, all constants mentioned in classical logic are presupposed to exist, while it makes no problems to speak about hypothetical objects in everyday language. These problems have been discussed in philosophical logic and some adequate manyvalued logics were developed to model these phenomena much better than classical firstorder logic can do. An adequate calculus, however, has not yet been given. Recent years have seen a thorough investigation of the framework of manyvalued truthfunctional logics. Unfortunately, restricted quantifications are not truthfunctional, hence they do not fit the framework directly. We solve this problem by applying recent methods from sorted logics.
Partiality without the Cost
 CADE13 WORKSHOP ON MECHANIZATION OF PARTIAL FUNCTIONS
, 1996
"... Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a threevalued logic decades ago, but there has not been a satisfactory mechanisatio ..."
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Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a threevalued logic decades ago, but there has not been a satisfactory mechanisation. Based on this, we have developed resolution and tableau calculi for automated theorem proving. The threevalued approach is more restrictive and allows rejecting certain unwanted formulae as faulty, which the simpler twovalued accept. It is commonly assumed that this finer analysis has to be payed for by greater computational complexity of proof search. However, for a large class of theorems that hold with respect to Kleene logic, the proofs can be transformed into classical ones and vice versa conserving the structure and size of the proof. Another main objective against a threevalued approach are the costs to implement a corresponding theorem prover. We show, that it is po...
Living with Paradoxes
"... A good knowledge representation system has to nd a balance between expressive power on the one hand and ecient reasoning on the other. Furthermore it is necessary to understand its limitations and problems. A logic which contains strings is very expressive and allows for very natural representation ..."
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A good knowledge representation system has to nd a balance between expressive power on the one hand and ecient reasoning on the other. Furthermore it is necessary to understand its limitations and problems. A logic which contains strings is very expressive and allows for very natural representations, which in turn allow for appropriate reasoning patterns. However, such a system has the feature that it is possible to formulate selfreferential paradoxes in it. This can be considered as a strength and as a weakness at the same time. On the one hand it is a positive aspect that it is possible to represent paradoxes, which can be formulated in natural language. On the other hand it is necessary to be careful and not to trivialise the logical system. In the paper dierent aspects of knowledge representation which allows selfreferentiality will be discussed. A system will be presented which is a pragmatic compromise between expressive power on the one hand and simplicity and eciency of the reasoning process on the other hand. It is built on a threevalued system that makes it possible to use reasoning techniques from classical rstorder logic.
URL:http://www.cs.bham.ac.uk/ A Resolution Calculus for
"... Abstract. The semantics of everyday language and the semantics of its naive translation into classical firstorder language considerably differ. An important discrepancy that is addressed in this paper is about the implicit assumption what exists. For instance, in the case of universal quantificatio ..."
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Abstract. The semantics of everyday language and the semantics of its naive translation into classical firstorder language considerably differ. An important discrepancy that is addressed in this paper is about the implicit assumption what exists. For instance, in the case of universal quantification natural language uses restrictions and presupposes that these restrictions are nonempty, while in classical logic it is only assumed that the whole universe is nonempty. On the other hand, all constants mentioned in classical logic are presupposed to exist, while it makes no problems to speak about hypothetical objects in everyday language. These problems have been discussed in philosophical logic and some adequate manyvalued logics were developed to model these phenomena much better than classical firstorder logic can do. An adequate calculus, however, has not yet been given. Recent years have seen a thorough investigation of the framework of manyvalued truthfunctional logics. Unfortunately, restricted quantifications are not truthfunctional, hence they do not fit the framework directly. We solve this problem by applying recent methods from sorted logics. 1
HigherOrder MultiValued Resolution
"... . This paper introduces a multivalued variant of higherorder resolution and proves it correct and complete with respect to a natural multivalued variant of Henkin's general model semantics. This resolution method is parametric in the number of truth values as well as in the particular choice ..."
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. This paper introduces a multivalued variant of higherorder resolution and proves it correct and complete with respect to a natural multivalued variant of Henkin's general model semantics. This resolution method is parametric in the number of truth values as well as in the particular choice of the set of connectives (given by arbitrary truth tables) and even substitutional quantifiers. In the course of the completeness proof we establish a model existence theorem for this logical system. The work reported in this paper provides a basis for developing higherorder mechanizations for many nonclassical logics. KEY WORDS: higherorder logic, resolution, multivalued, calculus 1 Introduction From the first attempts of modeling everyday reasoning within the framework of classical firstorder logic, it has been known that many relevant aspects cannot be adequately expressed in it. The attempts to cope with these aspects have lead to many specialized logics in the field of artificial in...