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Jeff B Paris - One of the best experts on this subject based on the ideXlab platform.
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an examination of the sep candidate anaLogical inference rule within pure Inductive Logic
Journal of Applied Logic, 2016Co-Authors: Elizabeth Howarth, Jeff B Paris, Alena VencovskaAbstract:Within the framework of (Unary) Pure Inductive Logic we investigate four possible formulations of a probabilistic principle of analogy based on a template considered by Paul Bartha in the Stanford Encyclopedia of Philosophy 1 and give some characterizations of the probability functions which satisfy them. In addition we investigate an alternative interpretation of anaLogical support, also considered by Bartha, based not on the enhancement of probability but on the creation of possibility.
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predicate exchangeability and language invariance in pure Inductive Logic
Logique Et Analyse, 2014Co-Authors: Malte S Klies, Jeff B ParisAbstract:In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language $L$ and replacing each occurrence of a predicate in an $L$-sentence $\phi$ according to this permutation should not change our belief in the truth of $\phi$. In this paper we study when a prior probability function $w$ on a purely unary language $L$ satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.
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the counterpart principle of anaLogical support by structural similarity
Erkenntnis, 2014Co-Authors: Alexandra Hill, Jeff B ParisAbstract:We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.
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from unary to binary Inductive Logic
Games Norms and Reasons -- Logic at the Crossroads; 09 Jan 2009-11 Jan 2009; Mumbai India. Heidelberg: Springer; 2011., 2011Co-Authors: Jeff B Paris, Alena VencovskaAbstract:Suppose you lived in a world of individuals \(a_1,a_2,a_3, \ldots\) (which exhaust the universe) and a finite set of predicates \(P(x), P_1(x),P_2(x), R(x,y), \ldots\) but no other constants or function symbols. You observe that \(P(a_1)\) and \(P(a_2)\) hold, and nothing else. In that case what probability, \(w(P(a_3))\) say, in terms of willingness to bet, should you assign to \(P(a_3)\) also holding?
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a survey of some recent results on spectrum exchangeability in polyadic Inductive Logic
Synthese, 2011Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
Alena Vencovska - One of the best experts on this subject based on the ideXlab platform.
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an examination of the sep candidate anaLogical inference rule within pure Inductive Logic
Journal of Applied Logic, 2016Co-Authors: Elizabeth Howarth, Jeff B Paris, Alena VencovskaAbstract:Within the framework of (Unary) Pure Inductive Logic we investigate four possible formulations of a probabilistic principle of analogy based on a template considered by Paul Bartha in the Stanford Encyclopedia of Philosophy 1 and give some characterizations of the probability functions which satisfy them. In addition we investigate an alternative interpretation of anaLogical support, also considered by Bartha, based not on the enhancement of probability but on the creation of possibility.
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from unary to binary Inductive Logic
Games Norms and Reasons -- Logic at the Crossroads; 09 Jan 2009-11 Jan 2009; Mumbai India. Heidelberg: Springer; 2011., 2011Co-Authors: Jeff B Paris, Alena VencovskaAbstract:Suppose you lived in a world of individuals \(a_1,a_2,a_3, \ldots\) (which exhaust the universe) and a finite set of predicates \(P(x), P_1(x),P_2(x), R(x,y), \ldots\) but no other constants or function symbols. You observe that \(P(a_1)\) and \(P(a_2)\) hold, and nothing else. In that case what probability, \(w(P(a_3))\) say, in terms of willingness to bet, should you assign to \(P(a_3)\) also holding?
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a survey of some recent results on spectrum exchangeability in polyadic Inductive Logic
Synthese, 2011Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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a characterization of the language invariant families satisfying spectrum exchangeability in polyadic Inductive Logic
Annals of Pure and Applied Logic, 2010Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.
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representation theorems for probability functions satisfying spectrum exchangeability in Inductive Logic
International Journal of Approximate Reasoning, 2009Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum exchangeability in polyadic Inductive Logic and give an application by characterizing those probability functions satisfying spectrum exchangeability which can be extended to a language with equality whilst still satisfying that property.
Kristian Kersting - One of the best experts on this subject based on the ideXlab platform.
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probabilistic Inductive Logic programming
Inductive Logic Programming, 2008Co-Authors: Kristian KerstingAbstract:Probabilistic Inductive Logic programming aka. statistical relational learning addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with machine learning and first order and relational Logic representations. A rich variety of different formalisms and learning techniques have been developed. A unifying characterization of the underlying learning settings, however, is missing so far. In this chapter, we start from Inductive Logic programming and sketch how the Inductive Logic programming formalisms, settings and techniques can be extended to the statistical case. More precisely, we outline three classical settings for Inductive Logic programming, namely learning from entailment, learning from interpretations, and learning from proofs or traces, and show how they can be adapted to cover state-of-the-art statistical relational learning approaches.
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probabilistic Inductive Logic programming
Algorithmic Learning Theory, 2004Co-Authors: Kristian KerstingAbstract:Probabilistic Inductive Logic programming, sometimes also called statistical relational learning, addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with first order Logic representations and machine learning. A rich variety of different formalisms and learning techniques have been developed. In the present paper, we start from Inductive Logic programming and sketch how it can be extended with probabilistic methods.
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probabilistic Inductive Logic programming
Lecture Notes in Computer Science, 2004Co-Authors: Kristian KerstingAbstract:Probabilistic Inductive Logic programming, sometimes also called statistical relational learning, addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with first order Logic representations and machine learning. A rich variety of different formalisms and learning techniques have been developed. In the present paper, we start from Inductive Logic programming and sketch how it can be extended with probabilistic methods. More precisely, we outline three classical settings for Inductive Logic programming, namely learning from entailment, learning from interpretations, and learning from proofs or traces, and show how they can be used to learn different types of probabilistic representations.
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towards combining Inductive Logic programming with bayesian networks
Inductive Logic Programming, 2001Co-Authors: Kristian Kersting, Luc De RaedtAbstract:Recently, new representation languages that integrate first order Logic with Bayesian networks have been developed. Bayesian Logic programs are one of these languages. In this paper, we present results on combining Inductive Logic Programming (ILP) with Bayesian networks to learn both the qualitative and the quantitative components of Bayesian Logic programs. More precisely, we show how to combine the ILP setting learning from interpretations with score-based techniques for learning Bayesian networks. Thus, the paper positively answers Koller and Pfeffer's question, whether techniques from ILP could help to learn the Logical component of first order probabilistic models.
Jurgen Landes - One of the best experts on this subject based on the ideXlab platform.
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a survey of some recent results on spectrum exchangeability in polyadic Inductive Logic
Synthese, 2011Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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a characterization of the language invariant families satisfying spectrum exchangeability in polyadic Inductive Logic
Annals of Pure and Applied Logic, 2010Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.
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representation theorems for probability functions satisfying spectrum exchangeability in Inductive Logic
International Journal of Approximate Reasoning, 2009Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum exchangeability in polyadic Inductive Logic and give an application by characterizing those probability functions satisfying spectrum exchangeability which can be extended to a language with equality whilst still satisfying that property.
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the principle of spectrum exchangeability within Inductive Logic
2009Co-Authors: Jurgen LandesAbstract:We investigate the consequences of the principle of Spectrum Exchangeability in Inductive Logic over the polyadic fragment of first order Logic. This principle roughly states that the probability of a possible world should only depend on how the inhabitants of this world behave with respect toindistinguishability. This principle is a natural generalization of exchangeability principles that have long been investigated over the monadic predicate fragment of first order Logic. It is grounded in our deep conviction that in the state of total ignorance all possible worlds that can be obtained from each other by basic symmetric transformations should have the same a priori probability. After first fixing our framework and showing some basic lemmata we prove that the principle of spectrum exchangeability implies several simple principles of exchangeability that are all based on our conviction that the probability functions should be invariant under basic renaming procedures. We then go on and show several representation theorems for the probability functions satisfying spectrum exchangeability. One of these representation results shows that we can represent the probability of sentences of a polyadic language in terms of the probability of sentences of a unary language. The other main representation result is a de Finetti-style result that shows that we can write every probability function satisfying spectrum exchangeability as an integral over some basic probability function weighted by a de Finetti prior µ. After that we use the de Finetti representation results to show a representation result for probability functions satisfying language invariance and spectrum exchangeability. Rather surprisingly it turns out that the notion of language invariance allows us to seamlessly extend our framework to the fragment of first order Logic containing the equality symbol and the predicate fragment. Thereafter we study principles that make Inductive assertions. We investigate the Paris Conjecture and we prove that in some instances the principle of instantial relevance holds for t−heterogeneous probability functions. However this principle fails for the completely independent function. Furthermore we show that the assumption of the principle of constant exchangeability and Johnsons’ sufficientness principle leads to only two trivial probability functions satisfying both these two principles.
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language invariance and spectrum exchangeability in Inductive Logic
European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 2007Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A sufficient condition, in terms of a de Finetti style representation, is given for a probability function in Inductive Logic (with relations of all arities) satisfying Spectrum Exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions. In contrast it is proved that (purely) t-heterogeneous probability functions can never be members of a language invariant family satisfying Spectrum Exchangeability.
Chiaki Sakama - One of the best experts on this subject based on the ideXlab platform.
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induction from answer sets in nonmonotonic Logic programs
ACM Transactions on Computational Logic, 2005Co-Authors: Chiaki SakamaAbstract: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.
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towards the integration of Inductive and nonmonotonic Logic programming
Discovery Science, 2002Co-Authors: Chiaki SakamaAbstract:Commonsense reasoning and machine learning are two important topics in AI. These techniques are realized in Logic programming as nonmonotonic Logic programming (NMLP) and Inductive Logic programming (ILP), respectively. NMLP and ILP have seemingly different motivations and goals, but they have much in common in the background of problems. This article overviews the author's recent research results for realizing induction from nonmonotonic Logic programs.
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nonmonotonic Inductive Logic programming
International Conference on Logic Programming, 2001Co-Authors: Chiaki SakamaAbstract:Nonmonotonic Logic programming (NMLP) and Inductive Logic programming (ILP) are two important extensions of Logic programming. The former aims at representing incomplete knowledge and reasoning with commonsense, while the latter targets the problem of Inductive construction of a general theory from examples and background knowledge. NMLP and ILP thus have seemingly different motivations and goals, but they have much in common in the background of problems, and techniques developed in each field are related to one another. This paper presents techniques for combining these two fields of Logic programming in the context of nonmonotonic Inductive Logic programming (NMILP). We review recent results and problems to realize NMILP.
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inverse entailment in nonmonotonic Logic programs
Lecture Notes in Computer Science, 2000Co-Authors: Chiaki SakamaAbstract:Inverse entailment (IE) is known as a technique for finding Inductive hypotheses in Horn theories. When a background theory is nonmonotonic, however, IE is not applicable in its present form. The purpose of this paper is extending the IE technique to nonmonotonic Inductive Logic programming (ILP). To this end, we first establish a new entailment theorem in normal Logic programs, then introduce the notion of contrapositive programs. Finally, a theory of IE in nonmonotonic ILP is constructed.