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46
Parametric Shape Analysis via 3Valued Logic
, 1999
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 539 (71 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
Bilattices and the Semantics of Logic Programming
, 1989
"... Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap's fourvalued logic, based on classical twovalued logic. Among other examples are those based on finite manyvalued logics, and on probabili ..."
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Cited by 380 (13 self)
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Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap's fourvalued logic, based on classical twovalued logic. Among other examples are those based on finite manyvalued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical twovalued setting, but the result provides a natural semantics for distributed logic programs, including those involving confidence factors. The classical twovalued and the Kripke/Kleene threevalued semantics become special cases, since the logics involved are natural sublogics of Belnap's logic, the logic given by the simplest bilattice. 1 Introduction Often useful information is spread over a number of sites ("Does anybody know, did Willie wear a hat when he left this morning?") that can be speci...
Bilattices In Logic Programming
, 1990
"... Bilattices, introduced by M. Ginsberg, constitute an elegant family of multiplevalued logics. Those meeting certain natural conditions have provided the basis for the semantics of a family of logic programming languages. Now we consider further restrictions on bilattices, to narrow things down to l ..."
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Cited by 42 (4 self)
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Bilattices, introduced by M. Ginsberg, constitute an elegant family of multiplevalued logics. Those meeting certain natural conditions have provided the basis for the semantics of a family of logic programming languages. Now we consider further restrictions on bilattices, to narrow things down to logic programming languages that can, at least in principle, be implemented. Appropriate bilattice background information is presented, so the paper is relatively selfcontained. 1 Introduction Logic programming is more than just Prolog. It is a distinctive way of thinking about computers and programming that has led to the creation of a whole family of programming languages, mostly experimental. Some time ago I found that bilattices provided a uniform semantics for a rich and interesting group of logic programming languages [9]. Bilattices are a natural generalization of classical twovalued logic, and were introduced by Matt Ginsberg in [12], and more fully in [13]. Recently I have found t...
Negation as Refutation
, 1989
"... A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A fourvalued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The f ..."
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Cited by 28 (5 self)
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A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A fourvalued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The fourvalued logic is a wellknown one, due to Belnap, and is the simplest example of Ginsberg's bilattice notion. An e#cient implementation based on semantic tableaux is sketched; it reduces to SLD resolution when negations are not involved. The resulting system can give reasonable answers to queries that involve both negation and free variables. Also it gives the same results as Prolog when there are no negations. Finally, an implementation in Prolog is given. 1 Introduction The most common treatment of negation in logic programming is negationasfailure. This leads to problems that are now familiar: meanings of programs become di#cult to specify; program operators need not reach fix...
Bilatticebased Logical Reasoning for Human Detection. CVPR
, 2007
"... The capacity to robustly detect humans in video is a critical component of automated visual surveillance systems. This paper describes a bilattice based logical reasoning approach that exploits contextual information and knowledge about interactions between humans, and augments it with the output of ..."
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Cited by 27 (6 self)
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The capacity to robustly detect humans in video is a critical component of automated visual surveillance systems. This paper describes a bilattice based logical reasoning approach that exploits contextual information and knowledge about interactions between humans, and augments it with the output of different low level detectors for human detection. Detections from low level partsbased detectors are treated as logical facts and used to reason explicitly about the presence or absence of humans in the scene. Positive and negative information from different sources, as well as uncertainties from detections and logical rules, are integrated within the bilattice framework. This approach also generates proofs or justifications for each hypothesis it proposes. These justifications (or lack thereof) are further employed by the system to explain and validate, or reject potential hypotheses. This allows the system to explicitly reason about complex interactions between humans and handle occlusions. These proofs are also available to the end user as an explanation of why the system thinks a particular hypothesis is actually a human. We employ a boosted cascade of gradient histograms based detector to detect individual body parts. We have applied this framework to analyze the presence of humans in static images from different datasets. 1.
A uniform approach to logic programming semantics
 Theory and Practice of Logic Programming
, 2005
"... ..."
Explanatory Update Theory: Applications of Counterfactual Reasoning to Causation
 Artificial Intelligence
, 1999
"... A stratified view of causal reasoning is set forth; one in which the identification of counterfactual dependencies plays an important role in determining what sort of causal connection, if any, exists between two events named by a given pair of partial descriptions. A semantics for temporal counterf ..."
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Cited by 14 (6 self)
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A stratified view of causal reasoning is set forth; one in which the identification of counterfactual dependencies plays an important role in determining what sort of causal connection, if any, exists between two events named by a given pair of partial descriptions. A semantics for temporal counterfactuals in which events are represented at the object level is then formalized based on a syntactic form of belief updating. Counterfactuals are evaluated relative to an agent's information state, taken to include a set of initial beliefs together with additional assumptions to handle the frame problem. Inertial inferences emerge as a sideeffect of requiring minimal information change between states of the world in some chronicle. A chronicle is, in addition, assumed minimal with respect to an explanatory preference that minimizes the set of beliefs that are not part of an agent's initial set of beliefs or are not supported by some body of lawlike knowledge. A number of epistemic preferenc...
Signed Formula Logic Programming: Operational Semantics and Applications
, 1995
"... . Signed formula can be used to reason about a wide variety of multiplevalued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in [26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint ..."
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Cited by 9 (0 self)
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. Signed formula can be used to reason about a wide variety of multiplevalued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in [26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint logic programming. Applications to bilattice logic programming and truthmaintenance are considered. Keywords: Logic for Artificial Intelligence, Multiplevalued Logic, Signed Formula, Constraint Logic Programming, TruthMaintenance, Bilattices * Please address all correspondence to: James Lu Department of Computer Science Bucknell University Lewisburg, PA 17837 U.S.A. Email: jameslu@bucknell.edu Phone: +1 717 524 1394 Fax: +1 717 524 1822 ** Work supported in part by the NSF under Grant CCR9225037. SIGNED FORMULA LOGIC PROGRAMMING 1 1. Introduction The logic of signed formulas facilitates the examination of questions regarding multiplevalued logics through classical logic. As...
Combinators for paraconsistent attitudes
 Logical Aspects of Computational Linguistics
, 2001
"... Abstract. In order to analyse the semantics of natural language sentences a translation into a partial type logic using lexical and logical combinators is presented. The sentences cover a fragment of English with propositional attitudes like knowledge, belief and assertion. A combinator is a closed ..."
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Cited by 8 (8 self)
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Abstract. In order to analyse the semantics of natural language sentences a translation into a partial type logic using lexical and logical combinators is presented. The sentences cover a fragment of English with propositional attitudes like knowledge, belief and assertion. A combinator is a closed term of the lambda calculus possibly containing lexical and/or logical constants. Such combinators seem promising from both a cognitive and computational point of view. There is approximately one lexical combinator for each word, but just eleven logical combinators for the present fragment. The partiality is only used for embedded sentences expressing propositional attitudes, thereby allowing for inconsistency without explosion (also called paraconsistency), and is based on a few key equalities for the connectives giving four truth values (truth, falsehood, and undefinedness with negative and positive polarity; only the first truth value is designated, i.e. yields the logical truths). 1
Semantic Minimization of 3Valued Propositional Formulae
 In Proc. Symp. on Logic in Comp. Sci
, 2002
"... This paper presents an algorithm for a nonstandard logicminimization problem that arises in 3valued propositional logic. The problem is motivated by the potential for obtaining better answers in applications that use 3valued logic. An answer of 0 or 1 provides precise (definite) information; an a ..."
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Cited by 7 (3 self)
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This paper presents an algorithm for a nonstandard logicminimization problem that arises in 3valued propositional logic. The problem is motivated by the potential for obtaining better answers in applications that use 3valued logic. An answer of 0 or 1 provides precise (definite) information; an answer of 1=2 provides imprecise (indefinite) information. By replacing a formula ' with a "better" formula , we may improve the precision of the answers obtained. In this paper, we give an algorithm that always produces a formula that is "best" (in a certain welldefined sense).