Computing only minimal answers in disjunctive deductive databases

A method is presented for computing minimal answers in disjunctive deductive databases under the disjunctive stable model semantics. Such answers are constructed by repeatedly extending partial answers. Our method is complete (in that every minimal answer can be computed) and does not admit redundancy (in the sense that every partial answer generated can be extended to a minimal answer), whence no non-minimal answer is generated. For stratified databases, the method does not (necessarily) require the computation of models of the database in their entirety. Compilation is proposed as a tool by which problems relating to computational efficiency and the non-existence of disjunctive stable models can be overcome. The extension of our method to other semantics is also considered.Comment: 48 page

Disjunctive bases: normal forms and model theory for modal logics

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it more thoroughly in its own right. We show that the presence of a disjunctive basis at the "one-step" level entails a number of good properties for a coalgebraic mu-calculus, in particular, a simulation theorem showing that every alternating automaton can be transformed into an equivalent nondeterministic one. Based on this, we prove a Lyndon theorem for the full fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform Interpolation result, for both the full mu-calculus and its fixpoint-free fragment, and a Janin-Walukiewicz-style characterization theorem for the mu-calculus under slightly stronger assumptions. We also raise the questions, when a disjunctive basis exists, and how disjunctive bases are related to Moss' coalgebraic "nabla" modalities. Nabla formulas provide disjunctive bases for many coalgebraic modal logics, but there are cases where disjunctive bases give useful normal forms even when nabla formulas fail to do so, our prime example being graded modal logic. We also show that disjunctive bases are preserved by forming sums, products and compositions of coalgebraic modal logics, providing tools for modular construction of modal logics admitting disjunctive bases. Finally, we consider the problem of giving a category-theoretic formulation of disjunctive bases, and provide a partial solution

The ss-semantics approach; theory and applications

AbstractThis paper is a general overview of an approach to the semantics of logic programs whose aim is to find notions of models which really capture the operational semantics, and are, therefore, useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (top-down) and a fixpoint (bottom-up) construction. It can also be characterized from the model-theoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version, and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semantics-based program transformation and analysis

A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic

Singapore National Research Foundatio

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table

Compositional Satisfiability Solving in Separation Logic

We introduce a novel decision procedure to the satisfiability problem in array separation logic combined with general inductively defined predicates and arithmetic. Our proposal differentiates itself from existing works by solving satisfiability through compositional reasoning. First, following Fermat’s method of infinite descent, it infers for every inductive definition a “base” that precisely characterises the satisfiability. It then utilises the base to derive such a base for any formula where these inductive predicates reside in. Especially, we identify an expressive decidable fragment for the compositionality. We have implemented the proposal in a tool and evaluated it over challenging problems. The experimental results show that the compositional satisfiability solving is efficient and our tool is effective and efficient when compared with existing solvers

Magic Sets for Disjunctive Datalog Programs

In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set (MS) optimization technique. An important feature of disjunctive Datalog is nonmonotonicity, which calls for nondeterministic implementations, such as backtracking search. A distinguishing characteristic of the new method is that the optimization can be exploited also during the nondeterministic phase. In particular, after some assumptions have been made during the computation, parts of the program may become irrelevant to a query under these assumptions. This allows for dynamic pruning of the search space. In contrast, the effect of the previously defined MS methods for disjunctive Datalog is limited to the deterministic portion of the process. In this way, the potential performance gain by using the proposed method can be exponential, as could be observed empirically. The correctness of MS is established thanks to a strong relationship between MS and unfounded sets that has not been studied in the literature before. This knowledge allows for extending the method also to programs with stratified negation in a natural way. The proposed method has been implemented in DLV and various experiments have been conducted. Experimental results on synthetic data confirm the utility of MS for disjunctive Datalog, and they highlight the computational gain that may be obtained by the new method w.r.t. the previously proposed MS methods for disjunctive Datalog programs. Further experiments on real-world data show the benefits of MS within an application scenario that has received considerable attention in recent years, the problem of answering user queries over possibly inconsistent databases originating from integration of autonomous sources of information.Comment: 67 pages, 19 figures, preprint submitted to Artificial Intelligenc