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Probabilistic argumentation systems
 Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 5: Algorithms for Uncertainty and Defeasible Reasoning
, 2000
"... Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [42]. More general approaches are the DempsterShafer theory of evidence [51], and possibility theory [16], which is closely re ..."
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Cited by 63 (35 self)
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Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [42]. More general approaches are the DempsterShafer theory of evidence [51], and possibility theory [16], which is closely related to fuzzy systems.
Probabilistic and TruthFunctional ManyValued Logic Programming
 IN PROCEEDINGS OF THE 29TH IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC
, 1998
"... We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that a ..."
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Cited by 13 (9 self)
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We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are Pcomplete for classical logic programs are shown to be coNPcomplete for probabilistic manyvalued logic programs. We then focus on manyvalued logic programming in Pr ? n as an approximation of probabilistic manyvalued logic programming. Surprisingly, manyvalued logic programs in Pr ? n have both a probabilistic semantics in probabilities over a set of possible worlds and a truthfunctional semantics in the finitevalued Łukasiewicz logics Łn . Moreover, manyvalued logic programming in Pr ? n has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming. We especially introduce the proof...
Anyworld assumptions in logic programming
, 2005
"... Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the C ..."
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Cited by 12 (3 self)
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Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the Closed World Assumption (CWA), which asserts that by default the truth of an atom is false. There is a second wellknown assumption, called Open World Assumption (OWA), which asserts that the truth of the atoms is supposed to be unknown by default. However, the CWA, the OWA and the combination of them are extremal, though important, assumptions over a large variety of possible assumptions on the truth of the atoms, whenever the truth is taken from an arbitrary truth space. The topic of this paper is to allow any assignment (i.e. interpretation), over a truth space, to be a default assumption. Our main result is that our extension is conservative in the sense that under the “everywhere false ” default assumption (CWA) the usual stable model semantics is captured. Due to the generality and the purely algebraic nature of our approach, it abstracts from the particular formalism of choice and the results may be applied in other contexts as well.
Building argumentation systems on set constraint logic
 Information, Uncertainty and Fusion
, 2000
"... The purpose of this paper is to show how the theory of probabilistic argumentation systems can be extended from propositional logic to the more general framework of set constraint logic. The strength of set constraint logic is that logical relations between nonbinary variables can be expressed more ..."
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The purpose of this paper is to show how the theory of probabilistic argumentation systems can be extended from propositional logic to the more general framework of set constraint logic. The strength of set constraint logic is that logical relations between nonbinary variables can be expressed more directly. This simplifies the classical way of modeling knowledge through propositional logic. Building argumentation systems on set constraint logic is therefore useful for improving its capabilities of expressing different forms of uncertain knowledge. 1
Consistency Reasoning in LatticeBased Fuzzy Description Logics
"... Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known ab ..."
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Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper we study the consistency problem for the fuzzy Description Logic LSHI and its sublogics in detail. The contribution of the paper is twofold. On the one hand, we provide a tableauxbased algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes, we also provide tight complexity bounds.
ESSLLI 1998 COURSE TableauBased Theorem Proving
, 1998
"... is allowed only with permission. The preliminary nature of this document entails that it has not been proof read by anyone else besides the author. The reader is advised to be aware of errors and omissions. Most, but not all material presented in the course is contained herein. Please report any err ..."
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is allowed only with permission. The preliminary nature of this document entails that it has not been proof read by anyone else besides the author. The reader is advised to be aware of errors and omissions. Most, but not all material presented in the course is contained herein. Please report any errors you may nd to reiner@ira.uka.de. 1
A Calculus for Interrogatives Based on Their Algebraic Semantics
"... We present a novel calculus for reasoning with both indicative and interrogative sentences, simultaneously modeling entailment between indicative sentences, entailment between interrogative sentences and answerhood relations. The logic is based on an interpretation of questions as entities of typ ..."
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We present a novel calculus for reasoning with both indicative and interrogative sentences, simultaneously modeling entailment between indicative sentences, entailment between interrogative sentences and answerhood relations. The logic is based on an interpretation of questions as entities of type t, the type of propositions. This is achieved by an algebraic reinterpretation of the domain of type t as a bilattice, rather than the standard boolean interpretation. We provide a Gentzen style axiomatization of the logic and prove its soundness and completeness with respect to the bilattice semantics. We also consider an alternative formulation using multivalued free variable firstorder tableaux, allowing for e#cient algorithmic proofsearch. We have implemented the tableau rules for the logic using a tableaubased theorem prover. Keywords: bilattice, logic, natural language, tableau, theoremprover 1 Introduction Entailment relations obviously play a key role in the semantic a...
Eliminating Variables in General Constraint Logic
"... Drawing inferences from a set of general constraint clauses is known as a difficult problem. A general approach is based on the idea of eliminating some or all variables involved. In the particular case of propositional logic, this approach leads to a simple procedure that incorporates the wellknow ..."
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Drawing inferences from a set of general constraint clauses is known as a difficult problem. A general approach is based on the idea of eliminating some or all variables involved. In the particular case of propositional logic, this approach leads to a simple procedure that incorporates the wellknown resolution principle. The purpose of this paper is to show how the resolution principle can be extended to constraint logic where the knowledge is given as a set of constraint clauses. The result is a general variable elimination method. The paper shows that the elimination problem can always be reduced to the problem of eliminating the variable from a (conjunctive) set of atomic constraints. Variabele elimination has a number of possible applications such as satisfiability testing, hypotheses testing, constraint solving, argumentative reasoning, and many others.