Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic context-free grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a first-order range-restricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform probability labels on each definition and near-maximal Bayes posterior probability and then 2) alters the probability labels to further increase the posterior probability. Stage 1) is implemented within CProgol4.5, which differs from previous versions of Progol by allowing user-defined evaluation functions written in Prolog. It is shown that maximising the Bayesian posterior function involves nding SLPs with short derivations of the examples. Search pruning with the Bayesian evaluation function is carried out in the same way as in previous versions of CProgol. The system is demonstrated with worked examples involving the learning of probability distributions over sequences as well as the learning of simple forms of uncertain knowledge.

We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the proposi-tional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by Dempster-Shafer belief functions. In both cases, we provide a complete axiomatiza-tion and show that the problem of deciding satistiability is NP-complete, no worse than that of propositional logic. As a tool for proving our complete axiomatiza-tions, we give a complete axiomatization for reasoning about Boolean combina-tions of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.

A global public-key infrastructure (PKI), components of which are emerging in the near future, is a prerequisite for security in distributed systems and for electronic commerce. The purpose of this paper is to propose an approach to modelling and reasoning about a PKI from a user Alice's point of view. Her view, from which she draws conclusions about the authenticity of other entities' public keys and possibly about the trustworthiness of other entities, consists of statements about which public keys she believes to be authentic and which entities she believes to be trustworthy, as well as a collection of certificates and recommendations obtained or retrieved from the PKI. The model takes into account recommendations for the trustworthiness of entities. Furthermore, it includes confidence values for statements and can exploit arbitrary certification structures containing multiple intersecting certification paths to achieve a higher confidence value than for any single c...

The term Soft Computing (SC) represents the combination of emerging problem-solving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, real-world problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagation-type algorithms.

Conditional probabilities are one promising and widely used approach to model uncertainty in information systems. This paper discusses the DUCK-calculus, which is founded on the cautious approach to uncertain probabilistic inference. Based on a set of sound inference rules derived probabilistic information is gained by local bounds propagation techniques. Precision being always a central point of criticism to such systems, we demonstrate that DUCK need not necessarily suffer from these problems. We can show that the popular Bayesian networks are subsumed by DUCK, implying that precise probabilities can be deduced by local propagation techniques, even in the multiply connected case. A comparative study with INFERNO and with inference techniques based on global operation-research techniques yields quite favorable results for our approach. Since conditional probabilities are also suited to model nonmonotonic situations by considering different contexts, we investigate the problems of maximal and relevant contexts, needed to draw default conclusions about individuals. 1 Wilhelm-Schickard-Institut, 2 Math.-Naturwiss. Fakultat, Universitat Tubingen, Universitat Augsburg, Sand 13, Universitatstr. 8, D-72076 Tubingen D-86135 Augsburg fthoenejguentzerg@informatik.uni-tuebingen.de wk@informatik.tu-muenchen.de 1 1.

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.

There are numerous applications where one agent a needs to reason about the beliefs of another agent, as well as about the actions that other agents may take. Eiter, Subrahmanian, and Pick (1998) introduced the concept of an agent program, and provided a language within which the operating principles of an agent could be declaratively encoded on top of imperative data structures. We first introduce certain belief data structures that an agent needs to maintain. Then we introduce the concept of a Meta Agent Program (map), that extends the (Eiter, Subrahmanian, and Pick 1998) framework, so as to allow agents to peform metareasoning. We build a formal semantics for maps, and show how this semantics supports not just beliefs agent a may have about agent b's state, but also beliefs about agents b's beliefs about agent c's actions, beliefs about b's beliefs about agent c's state, and so on. Finally, we provide a translation that takes any map as input and converts it into an agent program s...

This paper addresses the problem of bridging the gap between the fields of Knowledge Representation (KR) and Uncertain Reasoning (UR). The proposed solution consists of a framework for representing uncertain knowledge in which two components, one dealing with (categorical) knowledge and one dealing with uncertainty about this knowledge, are singled out. In this sense, the framework is "hybrid". This framework is characterized in both model-theoretic and prooftheoretic terms. State of belief is represented by "belief sets", defined in terms of the "functional approach to knowledge representation" suggested by Levesque. Examples are given, using first order logic and (a minimal subset of) M-Krypton for the KR side, and a yes/no trivial case and Dempster-Shafer theory for the UR side. 1. Introduction An impressive work has been carried out over the last two decades in the fields of Knowledge Representation (KR) and of Uncertain Reasoning (UR), resulting in a number of concepts being inv...

Stochastic Logic Programs (SLPs) are a generalisation of Hidden Markov Models (HMMs), stochastic context-free grammars, and undirected Bayes' nets. A pure stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0; 1] and C is a first-order range-restricted definite clause. SLPs have applications both as mechanisms for efficiently sampling from a given distribution and as representations for probabilistic knowledge. This paper discusses a distributional semantics for SLPs. Additionally two derivational mechanisms are introduced and analysed. These are 1) stochastic SLD (Selection-function-Linear-resolutionfor -Definite-clauses) refutation and 2) a program for enumerating the least Herbrand distributional model of an SLP in descending order. It is shown that as with logic programs unfolding transformations preserve the models of an SLP. Lastly, we discuss how Bayes' Theorem might be used to devise algorithms for learning SLPs. 1...

In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some well-known results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.