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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...
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 131 (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...
Hybrid Probabilistic Programs
 Journal of Logic Programming
, 1997
"... The precise probability of a compound event (e.g. e1 e2 ; e1 e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programmin ..."
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Cited by 70 (1 self)
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The precise probability of a compound event (e.g. e1 e2 ; e1 e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming [20, 19, 22, 23, 24] has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) have assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound ...
An Overview of Temporal and Modal Logic Programming
 Proc. First Int. Conf. on Temporal Logic  LNAI 827
, 1994
"... . This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)mo ..."
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Cited by 60 (6 self)
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. This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion. Categories: Temporal and Modal Logic Programming. 1 Introduction In logic programming, a program is a set of Horn clauses representing our knowledge and assumptions about some problem. The semantics of logic programs as developed by van Emden and Kowalski [96] is based on the notion of the least (minimum) Herbrand model and its fixedpoint characterization. As logic programming has been applied to a growing number of problem domai...
Probabilistic Deductive Databases
, 1994
"... Knowledgebase (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rulebased program ..."
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Cited by 57 (2 self)
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Knowledgebase (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rulebased programming, uncertainty, etc., offer a convenient framework for KB system development. But they require the user to be well versed with the low level details of system implementation. The manner in which uncertainty is handled has little mathematical basis. There is no decent notion of query optimization, forcing the user to take the responsibility for an efficient implementation of the KB system. We contend KB system development can and should take advantage of the deductive database technology, which overcomes most of the above limitations. An important problem here is to extend deductive databases into providing a systematic basis for rulebased programming with imperfect knowledge. In this paper, we are interested in an exension handling probabilistic knowledge.
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 52 (3 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
A Parametric Approach to Deductive Databases with Uncertainty
, 1997
"... Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules o ..."
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Cited by 44 (6 self)
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Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules of a program. On the basis of (iii), these frameworks can be classified into implication based (IB) and annotation based (AB) frameworks. In this paper, we develop a generic framework called the parametric framework as a unifying umbrella for IB frameworks. We develop the declarative, fixpoint, and prooftheoretic semantics of programs in the parametric framework and show their equivalence. Using this framework as a basis, we study the query optimization problem of containment of conjunctive queries in this framework, and establish necessary and sufficient conditions for containment for several classes of parametric conjunctive queries. Our results yield tools for use in the query optimization for large classes of query programs in IB deductive databases with uncertainty.
On A Theory of Probabilistic Deductive Databases
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2001
"... We propose a framework for modeling uncertainty where both belief and doubt can be given independent, firstclass status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the ..."
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Cited by 26 (0 self)
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We propose a framework for modeling uncertainty where both belief and doubt can be given independent, firstclass status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the form of a confidence level, consisting of a pair of intervals of probability, one for each of her belief and doubt. The space of confidence levels naturally leads to the notion of a trilattice, similar in spirit to Fitting's bilattices. Intuitively, the points in such a trilattice can be ordered according to truth, information, or precision. We develop a framework for probabilistic deductive databases by associating confidence levels with the facts and rules of a classical deductive database. While the trilattice structure offers a variety of choices for defining the semantics of probabilistic deductive databases, our choice of semantics is based on the truthordering, which we find to be closest to the classical framework for deductive databases. In addition to proposing a declarative semantics based on valuations and an equivalent semantics based on fixpoint theory, we also propose a proof procedure and prove it sound and complete. We show that while classical Datalog query programs have a polynomial time data complexity, certain query programs in the probabilistic deductive database framework do not even terminate on some input databases. We identify a large natural class of query programs of practical interest in our framework, and show that programs in this class possess polynomial time data complexity, i.e. not only do they terminate on every input database, they are guaranteed to do so in a number of steps polynomial in the input database size.
Hybrid Probabilistic Programs: Algorithms and Complexity
 In Proceedings UAI99
, 1999
"... 1 Introduction Computing the probability of a complex event from the probability of the primitive events constituting it depends upon the dependencies (if any) known to exist between the events being composed. For example, consider two events e1; e2. The probability, P(e1 ^ e2) of the occurrence of ..."
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Cited by 20 (3 self)
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1 Introduction Computing the probability of a complex event from the probability of the primitive events constituting it depends upon the dependencies (if any) known to exist between the events being composed. For example, consider two events e1; e2. The probability, P(e1 ^ e2) of the occurrence of both is events is 0 if the events are mutually exclusive. However, if the events are independent, then P(e1 ^ e2) = P(e1) \Theta P(e2). If we are ignorant of the relationship between these two events, then, as stated by Boole[1], the best we can say about P(e1 ^ e2) is that it lies in the interval [max(0; P(e1) + P(e2) \Gamma 1); min(P(e1); P(e2)]. In short, computing the probability of a complex event depends fundamentally upon our knowledge about the dependences between the events involved. In [2] we proposed a language called Hybrid Probabilistic (Logic)