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198
Probabilistic Logic Programming
, 1992
"... Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian ..."
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Cited by 133 (7 self)
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Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian [5, 6, 49, 50], Kifer et al [29, 30, 31]) have restricted themselves to nonprobabilistic semantical characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of [5, 6], but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad [16] for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth function...
Reconciling simplicity and likelihood principles in perceptual organization
 Psychological Review
, 1996
"... Two principles of perceptual organization have been proposed. The likelihood principle, following H. L. E yon Helmholtz ( 1910 / 1962), proposes that perceptual organization is chosen to correspond to the most likely distal layout. The simplicity principle, following Gestalt psychology, suggests tha ..."
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Cited by 69 (12 self)
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Two principles of perceptual organization have been proposed. The likelihood principle, following H. L. E yon Helmholtz ( 1910 / 1962), proposes that perceptual organization is chosen to correspond to the most likely distal layout. The simplicity principle, following Gestalt psychology, suggests that perceptual organization is chosen to be as simple as possible. The debate between these two views has been a central topic in the study of perceptual organization. Drawing on mathematical results in A. N. Kolmogorov's ( 1965)complexity heory, the author argues that simplicity and likelihood are not in competition, but are identical. Various implications for the theory of perceptual organization and psychology more generally are outlined. How does the perceptual system derive a complex and structured description of the perceptual world from patterns of activity at the sensory receptors? Two apparently competing theories of perceptual organization have been influential. The first, initiated by Helmholtz ( 1910/1962), advocates the likelihood principle: Sensory input will be organized into the most probable distal object or event consistent with that input. The second, initiated by Wertheimer and developed by other Gestalt psychologists, advocates what Pomerantz and Kubovy (1986) called the simplicity principle: The perceptual system is viewed as finding the simplest, rather than the most likely, perceptual organization consistent with the sensory input '. There has been considerable theoretical nd empirical controversy concerning whether likelihood or simplicity is the governing principle of perceptual organization (e.g., Hatfield, &
Feature Centrality and Conceptual Coherence
 Cognitive Science
, 1998
"... This paper has two objectives. First, we will argue that the mutability of conceptual fea tures can be represented as a single, multiplevalued dimension. We will show that the fea tures of a concept can be reliably ordered with respect to the degree to which people are willing to transform the fe ..."
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Cited by 63 (6 self)
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This paper has two objectives. First, we will argue that the mutability of conceptual fea tures can be represented as a single, multiplevalued dimension. We will show that the fea tures of a concept can be reliably ordered with respect to the degree to which people are willing to transform the feature while retaining the integrity of a representation; i.e., that a number of conceptual tasks, all of which require people to transform conceptual features, produce similar orderings. Following Medin and Shoben (1988), these tasks have in common that they ask people to consider an object that is missing a feature but is otherwise intact (e.g., a real chair without a seat)
Decidability of Model Checking for InfiniteState Concurrent Systems
 Acta Informatica
"... We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the ..."
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Cited by 59 (1 self)
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We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the state space. Therefore, they are inherently incapable of considering systems with infinitely many states. Recently, some new methods have been developed in order to at least palliate this problem. Using them, several verification problems for some restricted infinitestate models have been shown to be decidable. These results can be classified into those showing the decidability of equivalence relations [8, 9, 24, 26], and those showing the decidability of model checking for different modal and temporal logics. In this paper, we contribute to this second group. The model checking problem has been studied so far for three infinitestate models: contextfree processes, pushdown processes, and...
NonTuring Computers and NonTuring Computability
, 1994
"... possible to perform computational supertasks — that is, an infinite number of computational steps in a finite span of time — in a kind of relativistic spacetime that Earman and Norton (1993) have dubbed a MalamentHogarth spacetime1. ..."
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Cited by 38 (2 self)
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possible to perform computational supertasks — that is, an infinite number of computational steps in a finite span of time — in a kind of relativistic spacetime that Earman and Norton (1993) have dubbed a MalamentHogarth spacetime1.
Is the Brain a Digital Computer?
, 2004
"... This paper is about Cognitivism, and I had better say at the beginning what motivates it. If you read books about the brain (say Shepherd (1983) or Kuffler and Nicholls (1976)) you get a certain picture of what is going on in the brain. If you then turn to books about computation (say Boolos and Jef ..."
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Cited by 37 (0 self)
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This paper is about Cognitivism, and I had better say at the beginning what motivates it. If you read books about the brain (say Shepherd (1983) or Kuffler and Nicholls (1976)) you get a certain picture of what is going on in the brain. If you then turn to books about computation (say Boolos and Jeffrey, 1989) you get a picture of the logical structure of the theory of computation. If you then turn to books about cognitive science, (say Pylyshyn, 1985) they tell you that what the brain books describe is really the same as what the computability books were describing. Philosophically speaking, this does not smell right to me and I have learned, at least at the beginning of an investigation, to follow my sense of smell. II. The Primal Story I want to begin the discussion by trying to state as strongly as I can why cognitivism has seemed intuitively appealing. There is a story about the relation of human intelligence to computation that goes back at least to Turing's classic paper (1950), and I believe it is the foundation of the Cognitivist view. I will call it the Primal Story: We begin with two results in mathematical logic, the ChurchTuring thesis (or equivalently, the Churchs's thesis) and Turing's theorem. For our purposes, the ChurchTuring thesis states that for any algorithm there is some Turing machine that can implement that algorithm. Turing's thesis says that there is a Universal Turing Machine which can simulate any Turing Machine. Now if we put these two together we have the result that a Universal Turing Machine can implement any algorithm whatever. But now, what made this result so exciting? What made it send shivers up and down the spines of a whole generation of young workers in artificial intelligence is the following thought: Suppose the brain is a Un...
Algernon  A Tractable System for KnowledgeRepresentation
 SIGART BULLETIN
, 1991
"... AccessLimited Logic (ALL) is a theory of knowledge representation which formalizes the access limitations inherent in a network structured knowledgebase. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an accesslimited logic retrieves ..."
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Cited by 34 (9 self)
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AccessLimited Logic (ALL) is a theory of knowledge representation which formalizes the access limitations inherent in a network structured knowledgebase. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an accesslimited logic retrieves only those assertions reachable by following an available access path. The time complexity of inference in ALL is a polynomial function of the size of the accessible portion of the knowledgebase, rather than an exponential function of the size of the entire knowledgebase (as in much past work). AccessLimited Logic, though incomplete, still has a well defined semantics and a weakened form of completeness, Socratic Completeness, which guarantees that for any fact which is a logical consequence of the knowledgebase, there is a series of preliminary queries and assumptions after which a query of the fact will succeed. Algernon implements AccessLimited Logic. Algernon is impo...
Decidability and undecidability results for planning with numerical state variables
 Proceedings of the Sixth International Conference on Artificial Intelligence Planning and Scheduling
, 2002
"... These days, propositional planning can be considered a quite wellunderstood problem. Good algorithms are known that can solve a wealth of very different and sometimes challenging planning tasks, and theoretical computational properties of both general STRIPSstyle planning and the bestknown benchm ..."
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Cited by 28 (1 self)
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These days, propositional planning can be considered a quite wellunderstood problem. Good algorithms are known that can solve a wealth of very different and sometimes challenging planning tasks, and theoretical computational properties of both general STRIPSstyle planning and the bestknown benchmark problems have been established. However, propositional planning has a major drawback: The formalism is too weak to allow for the easy encoding of many genuinely interesting planning problems, specifically those involving numbers. A recent effort to enhance the PDDL planning language to cope with (among other additions) numerical state variables, to be used at the third international planning competition, has increased interest in these issues. In this contribution, we analyze “STRIPS with numbers” from a theoretical point of view. Specifically, we show that the introduction of numerical state variables makes the planning problem undecidable in the general case and many restrictions thereof and identify special cases for which we can provide decidability results.