We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of Fagin and Halpern from (J.ACM 41:340-367,1994). We define its syntax and semantics, and prove the strong completeness property of the corresponding axiomatic.
We propose a simple approach to combining rst-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a rst-order knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it species a ground Markov network containing one feature for each possible grounding of a rst.
We now review the basics of rst-order logic (FOL) and logic programming (LP). Readers familiar with FOL and LP can safely skip this section. 2.1 First-Order Logic (FOL) A term is a variable, a constant, or a functor applied to terms. An atom is of the form p(t 1;:::;t n) where p is a predicate of arity n and the t i are terms. A formula.
Markov logic networks (MLN) (Richardson and Domingos2006) and probabilistic soft logic (PSL) (Bach et al.2017) are notable SRL frameworks that define model structure with weighted first-order logic. However, specifying logical clauses for each problem is laborious and requires domain knowledge. The task of discovering these weighted clauses from data is referred to as.
The purpose of the present work is to define a formal logic, PrDL, with syntax deriving from Pratt's first-order dynamic logic ( 15 ), and semantics extending Kozen's semantics to formulas involving probabilistic programs. We give axioms and proof rules for this system, and show soundness and completeness relative to the underlying program free language, which is a certain extension of first.Learn More
In addition, two papers were nominated by Program Committee referees for the applications prize and two for the theory prize. The papers represent the div- sity and vitality in present ILP research including ILP theory, implementations, search and phase transition, distributed and large-scale learning, probabilistic ILP, biological applications, natural language learning and planning and.Learn More
This article mainly focuses on elucidating the Probabilistic Soft Logic (PSL), which is a joint probabilistic reasoning framework in detail. The overall intent of PSL is to have a way of evaluating how far an inferred, previously unseen fact, would hold true in a given domain. Hence, the general assumption is that the higher the inferred soft truth value, the higher the possibility of the fact.Learn More
Logic and Philosophy of Logic; Philosophy of Biology; Philosophy of Cognitive Science; Philosophy of Computing and Information; Philosophy of Mathematics; Philosophy of Physical Science; Philosophy of Social Science; Philosophy of Probability; General Philosophy of Science; Philosophy of Science, Misc; History of Western Philosophy. History of Western Philosophy; Ancient Greek and Roman.Learn More
In Information Retrieval (IR), probabilistic modelling relates to the use of a retrieval model that ranks documents in decreasing order of their estimated probability of relevance to a user’s information need expressed by a query. In an IR system based on a probabilistic model, the user is always guided to examine first the documents which are the most likely to be relevant to his or her need.Learn More
Indefinite probabilities are a novel technique for quantifying uncertainty, which were created as part of the PLN (Probabilistic Logic Networks) logical inference engine, which is a key component of the Novamente Cognition Engine (NCE), an integrative AGI system. Previous papers have discussed the use of indefinite probabilities in the context of a variety of logical inference rules, but have.Learn More
First-order logic adds the notion of terms, that is, expressions referring to objects; a term is a constant symbol, a logical variable, or a k-ary function applied to k terms as arguments. Proposition symbols are replaced by atomic sentences, consisting of either predicate symbols applied to terms or equality between terms. Thus.Learn More
It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of.Learn More
This papers investigates the manipulation of statements of strong in- dependence in probabilistic logic. Inference methods based on polynomial pro- gramming are presented for strong independence.Learn More
Term. Hilary Term 2017 (16 lectures) Overview. Logic plays an important role in many disciplines, including Philosophy and Mathematics, but it is particularly central to Computer Science. This course emphasises the computational aspects of logic, including applications to databases, constraint solving, programming and automated verification, among many others. We also highlight algorithmic.Learn More
Forthcoming Papers R. Greiner, PALO: a probabilistic hill-climbing algorithm Many learning systems search through a space of possible performance elements, seeking an element whose expected utility, over the distribution of problems, is high. As the task of finding the globally optimal element is often intractable, many practical learning systems instead hill-climb to a local optimum.Learn More
We expect that observations of this kind will support the discussion of both formal and common sense properties of probabilistic first-order inference in general and inference according to the principle of maximum entropy in a first-order setting in particular. Acknowledgments. We would like to thank the anonymous referees of this paper for their helpful comments and valuable suggestions.Learn More