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37
Theory of Generalized Annotated Logic Programming and its Applications
 Journal of Logic Programming
, 1992
"... Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to ..."
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Cited by 170 (21 self)
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Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 32, 47, 40, 18] as well as some formalisms for temporal reasoning [1, 3, 42] are shown to fit into this framework. As an interesting byproduct of this investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilatticebased logic programming, which until now has not been characterized modeltheoretically. This is accompanied by a corresponding proof theory. 1 Introduction Large knowledge bases can be inconsistent in many ways. Nevertheless, certain...
An Illative Theory of Relations
, 1990
"... this paper we present a nonstandard logic for our structures. It is a typefree intensional logic, and is also in the tradition of Curry's illative logic [HS86]; see also [AczN, FM87, Smi84, MA88]. The logic has two judgments: that an object is a fact and that an object is a stateofa#airs (cf. tr ..."
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Cited by 15 (2 self)
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this paper we present a nonstandard logic for our structures. It is a typefree intensional logic, and is also in the tradition of Curry's illative logic [HS86]; see also [AczN, FM87, Smi84, MA88]. The logic has two judgments: that an object is a fact and that an object is a stateofa#airs (cf. truth and proposition). Objects are given using a variant of the traditional situation theory notation which is more standard, logically speaking, with explicit negation and quantification (see also [Bar87]). No metalinguistic apparatus is employed
The semantic paradoxes and the paradoxes of vagueness
, 2003
"... Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic para ..."
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Cited by 13 (6 self)
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Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. There is also some temptation to connect up the two cases, by viewing the semantic paradoxes as due to something akin to vagueness or indeterminacy in semantic concepts like ‘true’. The thought is that the notion of truth is introduced by a schema that might initially appear to settle its extension uniquely:
A Cutfree Sequent Calculus for Elementary Situated Reasoning
, 1991
"... A rstorder language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to include formulae of the form t : (where t is a term and is a formula) meaning that is true in the s ..."
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Cited by 10 (3 self)
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A rstorder language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to include formulae of the form t : (where t is a term and is a formula) meaning that is true in the situation referred to by t. Gentzen's sequent calculus for classical rstorder logic is extended with rules which capture this interpretation. Variants of the calculus and extensions of the language are discussed and the Cut rule is shown to be eliminable from some of the proposed calculi. Situation theory has been concerned with a range of issues centring around the partiality, context dependency and intensional structure of information. In formalizing situation theory one must focus on a specic aspect of the whole package  there is too much uncertainty and equivocation about the connections between the various parts. A dominant approach in recent years has been to focus on build...
A Logic Of Vision
"... This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and JohnsonLaird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessari ..."
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Cited by 7 (0 self)
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This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and JohnsonLaird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessarily differs from situation semantics. On the psychological side, our main inspiration is Marr's (1982) theory of vision, which can easily accomodate fallible perception. In Marr's theory, vision is a multilayered process. The different layers have filters of different gradation, wkich makes vision at each of them approximate. On the logical side, our task is therefore twofold to fomalise the layers and the ways in which they may refine each other, and to develop logical means to let description vary with such degrees of refinement.
Solving the Paradoxes, escaping revenge
 THE REVENGE OF THE LIAR
"... It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no h ..."
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Cited by 7 (1 self)
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It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad hoc means to avoid them. Others (“dialetheists”) argue that we can put the paradoxes to rest, but only by licensing the acceptance of some contradictions (presumably in a paraconsistent logic that prevents the contradictions from spreading everywhere). I think the received wisdom is incorrect. In my effort to rebut it, I will focus on a certain type of solution to the paradoxes. This type of solution has the advantage of keeping the full Tarski truth schema (T) True(hAi) ↔ A (and more generally, a full satisfaction schema). This has a price, namely that
Commonsense set theory
 MetaLevel Architectures and Reflection. North
, 1988
"... Abstract: It is argued that set theory provides a powerful addition to commonsense reasoning, facilitating expression of metaknowledge, names, and selfreference. Difficulties in establishing a suitable language to include sets for such purposes are discussed, as well as what appear to be promising ..."
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Cited by 6 (4 self)
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Abstract: It is argued that set theory provides a powerful addition to commonsense reasoning, facilitating expression of metaknowledge, names, and selfreference. Difficulties in establishing a suitable language to include sets for such purposes are discussed, as well as what appear to be promising solutions. Ackermann’s set theory as well as a more recent theory involving universal sets are discussed in terms of their relevance to commonsense.
Intensionality and Coercion
 ASL Lecture Notes in Logic, A.K. Peters
, 2002
"... This paper will appear in R. Kahle (ed.), Intensionality, ASL Lecture Notes in Logic, AK Peters ..."
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Cited by 4 (2 self)
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This paper will appear in R. Kahle (ed.), Intensionality, ASL Lecture Notes in Logic, AK Peters
Approximate Databases: A Support Tool for Approximate Reasoning
"... ABSTRACT. This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database (AKDB), based on a semantics inspired by rough sets. The implementation is based upon the use of a standard SQL database to store logical facts, augmented with severa ..."
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Cited by 3 (0 self)
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ABSTRACT. This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database (AKDB), based on a semantics inspired by rough sets. The implementation is based upon the use of a standard SQL database to store logical facts, augmented with several query interface layers implemented in JAVA through which extensional, intensional and local closed world nonmonotonic queries in the form of crisp or approximate logical formulas can be evaluated tractably. A graphical database design user interface is also provided which simplifies the design of databases, the entering of data and the construction of queries. The theory and semantics for AKDBs is presented in addition to application examples and details concerning the database implementation.