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Induction from answer sets in nonmonotonic logic programs
 ACM Transactions on Computational Logic
"... Inductive logic programming (ILP) realizes inductive machine learning in computational logic. However, the present ILP mostly handles classical clausal programs, especially Horn logic programs, and has limited applications to learning nonmonotonic logic programs. This article studies a method for re ..."
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Inductive logic programming (ILP) realizes inductive machine learning in computational logic. However, the present ILP mostly handles classical clausal programs, especially Horn logic programs, and has limited applications to learning nonmonotonic logic programs. This article studies a method for realizing induction in nonmonotonic logic programs. We consider an extended logic program as a background theory, and introduce techniques for inducing new rules using answer sets of the program. The produced new rules explain positive/negative examples in the context of inductive logic programming. The proposed methods extend the present ILP techniques to a syntactically and semantically richer framework, and contribute to a theory of nonmonotonic ILP.
The plausibilityinformativeness theory
 In V. F. Hendricks & D. Pritchard (Eds.), New waves in epistemology. Aldershot: Ashgate
"... ..."
C.: A Unified Treatment of Knowledge Dynamics
 In: International Conference on the Principles of Knowledge Representation and Reasoning, KR 2004
, 2004
"... Using morphologics we show how to find explanations of observations, how to perform revision, contraction, fusion, in an unified way. In the framework of abduction, we show how to deal with observations inconsistent with the background theory and introduce methods to treat multiple observations. ..."
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Using morphologics we show how to find explanations of observations, how to perform revision, contraction, fusion, in an unified way. In the framework of abduction, we show how to deal with observations inconsistent with the background theory and introduce methods to treat multiple observations. Based on these ideas we introduce a dynamics for transforming the background theory in function of observations.
Probabilistic Reasoning With Terms
, 2002
"... Many problems in artificial intelligence can be naturally approached by generating and manipulating probability distributions over structured objects. In this paper we represent structured objects by firstorder logic terms (lists, trees, tuples, and nestings thereof) and higherorder terms (sets, m ..."
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Many problems in artificial intelligence can be naturally approached by generating and manipulating probability distributions over structured objects. In this paper we represent structured objects by firstorder logic terms (lists, trees, tuples, and nestings thereof) and higherorder terms (sets, multisets), and we study the question how to define probability distributions over such terms. We present two Bayesian approaches that employ such probability distributions over structured objects: the first is an upgrade of the wellknown naive Bayesian classifier to deal with firstorder and higherorder terms, and the second is an upgrade of propositional Bayesian networks to deal with nested tuples.
2007a), The Logic of Theory Assessment
 the Journal of Philosophical Logic
"... ABSTRACT. This paper starts by indicating the analysis of Hempel_s conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausi ..."
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ABSTRACT. This paper starts by indicating the analysis of Hempel_s conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel_s cake and eat it too V in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, a is an acceptable theory for evidence b if and only if a is both sufficiently plausible given b and sufficiently informative about b. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibilityinformativeness approach to Carnap_s positive relevance account, thereby shedding new light on Carnap_s analysis as well as solving another problem of confirmation theory. KEY WORDS: confirmation theory, consequence relations, plausibilityinformativeness theory, probability measures, ranking functions, theory assessment
Assessing theories, Bayes style
 Synthese
, 2008
"... Abstract The problem addressed in this paper is "the main epistemic problem concerning science", viz. "the explication of how we compare and evaluate theories [...] in the light of the available evidence " (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. E ..."
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Abstract The problem addressed in this paper is "the main epistemic problem concerning science", viz. "the explication of how we compare and evaluate theories [...] in the light of the available evidence " (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 2742). Minneapolis: University of Minnesota Press). Sections 1 3 contain the general plausibilityinformativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: truth and informativenessmeasured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective proba
DOI 10.1007/s1109800791112 Hempel’s logic of confirmation
"... Abstract This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 ..."
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Abstract This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel’s cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap’s analysis. 1 Hempel’s conditions of adequacy In his ‘‘Studies in the Logic of Confirmation’ ’ (1945) Carl G. Hempel presented the following conditions of adequacy for any relation of confirmation (names for 3.1 and 3.2 added). For any sentence (observation report) E and any sentences (hypotheses) H, H0:
ORIGINAL PAPER Assessing theories, Bayes style
"... Abstract The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence ” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing ..."
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Abstract The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence ” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1–3 contain the general plausibilityinformativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities.
Modern Logic and Its Role in the Study of Knowledge
"... y the kind of inductive reasoning involved in experimental sciences as eagerly as he would investigate the kind of reasoning that is employed in mathematical proofs. However, in the last century logic seems to have developed into a relatively specialised and not seldomly obscure branch of mathematic ..."
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y the kind of inductive reasoning involved in experimental sciences as eagerly as he would investigate the kind of reasoning that is employed in mathematical proofs. However, in the last century logic seems to have developed into a relatively specialised and not seldomly obscure branch of mathematics. This is all the more paradoxical since the first half of the 20 century has often been called `the Golden Age of logic'. Following the pioneering work of Gottlob Frege, who developed a forerunner of predicate logic called Begriffschrift (`concept language') in 1893, Russell and Whitehead published their threevolume Principia Mathematica between 1910 and 1913, in which they reestablished the foundations of pure mathematics in logical terms. Whereas Kurt Gdel dealt a severe blow to the ambitions of logicians when he demonstrated that any logical system powerful enough to include natural numbers is also necessarily incomplete (i.e., the logical system allows the formulation of true stat