The expressiveness of Datalog cicuits (DAC) (original) (raw)

Circumscribing DATALOG: Expressive Power and Complexity

Theoretical Computer Science, 1998

In this paper we study a generalization of DATALOG, the language of function-free definite clauses. It is known that standard DATALOG semantics (i.e., least Herbrand model semantics) can be obtained by regarding programs as theories to be circumscribed with all predicates to be minimized. The extension proposed here, called DATALOG~!~~, consists in considering the general form of circumscription, where some predicates are minimized, some predicates are fixed, and some vary. We study the complexity and the expressive power of the language thus obtained. We show that this language (and, actually, its non-recursive fragment) is capable of expressing all the queries in DB-co-m and, as such, is much more powerful than standard DATALOG, whose expressive power is limited to a strict subset of PTIME queries. Both data and combined complexities of answering DATALOGCIRC queries are studied. Data complexity is proved to be co-NP-complete. Combined complexity is shown to be in general hard for co-NE and complete for co-NE in the case of Herbrand bases containing k distinct constant symbols, where k is bounded.

More on tractable disjunctive Datalog

The Journal of Logic Programming, 2000

Sometimes it is more natural to express knowledge in disjunctive Datalog rather than in ordinary Datalog. Several highly complex variants of disjunctive Datalog have been proposed in the past and their expressive power has been studied. In this paper we investigate tractable fragments of disjunctive Datalog. Algorithms are presented to answer queries de®ned using these fragments and their complexity analyzed. Furthermore, the expressive power of these tractable subsets is studied. The most expressive of the languages considered here is shown to express, in some sense explained in the paper, all polynomial time queries. This is the ®rst identi®ed fragment of disjunctive Datalog with this property.

Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues

Theory and Practice of Logic Programming, 2012

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming of Datalog-based languages became evident, e.g. in the context of data-integration (consistent query-answering, ontology-based data access) and Semantic Web applications: The language does not permit any generation of and reasoning with unnamed individuals in an obvious way. In general, it is weak in supporting many cases of existential quantification. To overcome this problem, Datalog ∃ has recently been proposed, which extends traditional Datalog by existential quantification in rule heads. In this work, we propose a natural extension of Disjunctive Datalog and Datalog ∃ , called Datalog ∃,∨ , which allows both disjunctions and existential quantification in rule heads and is therefore an attractive language for knowledge representation and reasoning, especially in domains where ontology-based reasoning is needed. We formally define syntax and semantics of the language Datalog ∃,∨ , and provide a notion of instantiation, which we prove to be adequate for Datalog ∃,∨ . A main issue of Datalog ∃ and hence also of Datalog ∃,∨ is that decidability is no longer guaranteed for typical reasoning tasks. In order to address this issue, we identify many decidable fragments of the language, which extend, in a natural way, analog classes defined in the non-disjunctive case. Moreover, we carry out an in-depth complexity analysis, deriving interesting results which range from Logarithmic Space to Exponential Time.

Datalog Rewritability of Disjunctive Datalog Programs and its Applications to Ontology Reasoning

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog-a novel rule-based KR language that extends both datalog and linear disjunctive datalog and for which reasoning is tractable in data complexity. We then explore applications of weakly linear programs to ontology reasoning and propose a tractable extension of OWL 2 RL with disjunctive axioms. Our empirical results suggest that many non-Horn ontologies can be reduced to weakly linear programs and that query answering over such ontologies using a datalog engine is feasible in practice.

The Expressive Powers of Stable Models for Bound and Unbound DATALOG Queries

Journal of Computer and System Sciences, 1997

Various types of stable models are known in the literature: T-stable (total stable), P-stable ( partial stable, also called three-valued stable), M-stable (maximal stable, also known under various different names), and L-stable (least undefined stable). For each type of stable model, the paper analyzes two versions of deterministic semantics: possible semantics, which is based on the union of all stable models of the given type, and definite semantics, which is instead based on their intersection and is like classical certain semantics except that it makes no inference if no model exists. For total stable models, which are the only type of stable models whose existence is not guaranteed for every program, certain semantics is taken into account as well. The expressive powers of each type of stable model under the above versions of semantics are investigated for both bound (i.e., ground) and unbound queries on DATALOG programs with negation. As deterministic semantics is argued to be inappropriate for unbound queries, a nondeterministic semantics is also proposed for them and its expressive power is fully characterized as well. ] 1997 Academic Press * Work partially supported by the ECUS033 project``DEUS EX MACHINA: Non-determinism in deductive databases'' and by a MURST grant (40 0 share) under the project``Sistemi formali e strumenti per basi di dati evolute''. An extended abstract of the preliminary results about bound queries appears in the informal proceedings of the Workshop oǹ`S tructural Complexity and Recursion-Theoretic Methods in Logic Programming'' (Vancouver, October 1993) and an extended abstract of the preliminary results about unbound queries appears in the proceedings of the conference ICDT'95 (Prague, January 1995).

Rewriting Ontological Queries into Small Nonrecursive Datalog Programs

arXiv (Cornell University), 2011

We consider the setting of ontological database access, where an Abox is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a T-box Σ formulated in DL-Lite or Linear Datalog ±. It is well-known that (Σ, q) can be rewritten into an equivalent nonrecursive Datalog program P that can be directly evaluated over D. However, for Linear Datalog ± or for DL-Lite versions that allow for role inclusion, the rewriting methods described so far result in a nonrecursive Datalog program P of size exponential in the joint size of Σ and q. This gives rise to the interesting question of whether such a rewriting necessarily needs to be of exponential size. In this paper we show that it is actually possible to translate (Σ, q) into a polynomially sized equivalent nonrecursive Datalog program P .

On the Equivalence of Recursive and Nonrecursive Datalog Programs

Journal of Computer and System Sciences, 1997

We study the problem of determining whether a given recursive Datalog program is equivalent to a given nonrecursive Datalog program. Since nonrecursive Datalog programs are equivalent to unions of conjunctive queries, we study also the problem of determining whether a given recursive Datalog program is contained in a union of conjunctive queries. For this problem, we prove doubly exponential upper and lower time bounds. For the equivalence problem, we prove triply exponential upper and lower time bounds.

Datalog and description logics: Expressive power

1998

Recently there was some attention on integration of description logics of the AL-family with rule-based languages for querying relational databases such as Datalog, so as to achieve the best characteristics of both kinds of formalisms in a common framework. Formal analysis on such hybrid languages has been limited to computational complexity: ie, how much time/space it is needed to answer to a specific query?

Rewriting Guarded Existential Rules into Small Datalog Programs

2018

The goal of this paper is to understand the relative expressiveness of the query language in which queries are specified by a set of guarded (disjunctive) tuple-generating dependencies (TGDs) and an output (or 'answer') predicate. Our main result is to show that every such query can be translated into a polynomially-sized (disjunctive) Datalog program if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant. To overcome the challenge that Datalog has no direct means to express the existential quantification present in TGDs, we define a two-player game that characterizes the satisfaction of the dependencies, and design a Datalog query that can decide the existence of a winning strategy for the game. For guarded disjunctive TGDs, we can obtain Datalog rules with disjunction in the heads. However, the use of disjunction is limited, and the resulting rules fall into a fragment that can be evaluated in deterministic single exponential time. We proceed...