Semistructured data is characterized by the lack of any fixed and rigid schema, although typically the data has some implicit structure. While the lack of fixed schema makes extracting semistructured data fairly easy and an attractive goal, presenting and querying such data is greatly impaired. Thus, a critical problem is the discovery of the structure implicit in semistructured data and, subsequently, the recasting of the raw data in terms of this structure. In this paper, we consider a very general form of semistructured data based on labeled, directed graphs. We show that such data can be typed using the greatest fixpoint semantics of monadic datalog programs. We present an algorithm for approximate typing of semistructured data. We establish that the general problem of finding an optimal such typing is NP-hard, but present some heuristics and techniques based on clustering that allow efficient and near-optimal treatment of the problem. We also present some preliminary experimental results.

Groote and Vaandrager introduced the tyft/tyxt format for Transition System Specifications (TSSs), and established that for each TSS in this format that is well-founded, the bisimulation equivalence it induces is a congruence. In this paper, we construct for each TSS in tyft/tyxt format an equivalent TSS that consists of tree rules only. As a corollary we can give an affirmative answer to an open question, namely whether the well-foundedness condition in the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates. 1

. We present a new approach to probabilistic logic programs with a possible worlds semantics. Classical program clauses are extended by a subinterval of [0; 1] that describes the range for the conditional probability of the head of a clause given its body. We show that deduction in the defined probabilistic logic programs is computationally more complex than deduction in classical logic programs. More precisely, restricted deduction problems that are Pcomplete for classical logic programs are already NP-hard for probabilistic logic programs. We then elaborate a linear programming approach to probabilistic deduction that is efficient in interesting special cases. In the best case, the generated linear programs have a number of variables that is linear in the number of ground instances of purely probabilistic clauses in a probabilistic logic program. 1 INTRODUCTION There is already a quite extensive literature on probabilistic propositional logics and their various dialects. The most fa...

We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M , if M C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudo-boolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the one-step provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.

We give a general framework for developing the least model semantics, xpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rst-order Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multi-degree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multi-agent systems.

This paper completes an investigation of the logical expressibility of finite, locally stratified, general logic programs. We show that every hyperarithmetic set can be defined by a suitably chosen locally stratified logic program (as a set of values of a predicate over its perfect model). This is an optimal result, since the perfect model of a locally stratified program is itself an implicitly definable hyperarithmetic set (under a recursive coding of the Herbrand base); hence to

Induction of recursive theories in the normal ILP setting is a difficult learning task whose complexity is equivalent to multiple predicate learning. In this paper we propose computational solutions to some relevant issues raised by the multiple predicate learning problem. A separate-andparallel -conquer search strategy is adopted to interleave the learning of clauses supplying predicates with mutually recursive definitions. A novel generality order to be imposed on the search space of clauses is investigated, in order to cope with recursion in a more suitable way. The consistency recovery is performed by reformulating the current theory and by applying a layering technique, based on the collapsed dependency graph. The proposed approach has been implemented in the ILP system ATRE and tested on some laboratory-sized and real-world data sets. Experimental results demonstrate that ATRE is able to learn correct theories autonomously and to discover concept dependencies. Finally, related works and their main differences with our approach are discussed.

In this paper, we describe a methodology for proving termination of logic programs. First, we introduce U-graphs as an abstraction of logic programs and establish that SLDNFderivations can be realized by instances of paths in the U-graphs. Such a relation enables us to use U-graphs for establishing the universal termination of logic programs. In our method, we associate pre- and post-assertions to the nodes of the graph and ordered assertions to selected edges of the graph. With this as the basis, we develop a simple method for establishing the termination of logic programs. The simplicity/practicality of the method is illustrated through examples. 1 Introduction One of the most important features of logic programming is its declarative semantics. That is, one can consider the programs to be self-specifying as they are non-procedural, and hence do not need elaborate correctness proofs. There can be a debate about whether it is meaningful to talk about verifying logic programs. It wil...

We give a general framework for developing the least model semantics, xpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rst-order Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multi-degree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multi-agent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLD-resolution calculi proposed for them are more eective.

We propose a modal query language called MDatalog. A rule of an MDatalog program is a universally quantified modal Horn clause. This language is interpreted in fixed-domain first-order modal logics over signatures without functions. We give algorithms to construct the least models for MDatalog programs. We show PTIME complexity of computing queries for a given MDatalog program in the logics KD, T , KB, KDB, B, K5, KD5, K45, KD45, KB5, and S5, provided that the quantifier depths of queries and the program are finitely bounded, and that the modal depth of the program is finitely bounded in the case when the considered logic is not an extension of K5. Some examples are given to illustrate application of the techniques to reason about belief and knowledge.