177,455 research outputs found
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
First-Order Query Evaluation with Cardinality Conditions
We study an extension of first-order logic that allows to express cardinality
conditions in a similar way as SQL's COUNT operator. The corresponding logic
FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query
evaluation for this logic is fixed-parameter tractable on classes of structures
(or databases) of bounded degree. In the present paper, we first show that the
fixed-parameter tractability of FOC(P) cannot even be generalised to very
simple classes of structures of unbounded degree such as unranked trees or
strings with a linear order relation.
Then we identify a fragment FOC1(P) of FOC(P) which is still sufficiently
strong to express standard applications of SQL's COUNT operator. Our main
result shows that query evaluation for FOC1(P) is fixed-parameter tractable
with almost linear running time on nowhere dense classes of structures. As a
corollary, we also obtain a fixed-parameter tractable algorithm for counting
the number of tuples satisfying a query over nowhere dense classes of
structures
Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting
In this paper we study lifted inference for the Weighted First-Order Model
Counting problem (WFOMC), which counts the assignments that satisfy a given
sentence in first-order logic (FOL); it has applications in Statistical
Relational Learning (SRL) and Probabilistic Databases (PDB). We present several
results. First, we describe a lifted inference algorithm that generalizes prior
approaches in SRL and PDB. Second, we provide a novel dichotomy result for a
non-trivial fragment of FO CNF sentences, showing that for each sentence the
WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we
prove that, in the first case our algorithm solves the WFOMC problem in PTIME,
and in the second case it fails. Third, we present several properties of the
algorithm. Finally, we discuss limitations of lifted inference for symmetric
probabilistic databases (where the weights of ground literals depend only on
the relation name, and not on the constants of the domain), and prove the
impossibility of a dichotomy result for the complexity of probabilistic
inference for the entire language FOL
Order Invariance on Decomposable Structures
Order-invariant formulas access an ordering on a structure's universe, but
the model relation is independent of the used ordering. Order invariance is
frequently used for logic-based approaches in computer science. Order-invariant
formulas capture unordered problems of complexity classes and they model the
independence of the answer to a database query from low-level aspects of
databases. We study the expressive power of order-invariant monadic
second-order (MSO) and first-order (FO) logic on restricted classes of
structures that admit certain forms of tree decompositions (not necessarily of
bounded width).
While order-invariant MSO is more expressive than MSO and, even, CMSO (MSO
with modulo-counting predicates), we show that order-invariant MSO and CMSO are
equally expressive on graphs of bounded tree width and on planar graphs. This
extends an earlier result for trees due to Courcelle. Moreover, we show that
all properties definable in order-invariant FO are also definable in MSO on
these classes. These results are applications of a theorem that shows how to
lift up definability results for order-invariant logics from the bags of a
graph's tree decomposition to the graph itself.Comment: Accepted for LICS 201
Fixpoints and Bounded Fixpoints for Complex Objects
We investigate a query language for complex-object databases, which is designed to (1) express only tractable queries, and (2) be as expressive over flat relations as first order logic with fixpoints. The language is obtained by extending the nested relational algebra NRA with a bounded fixpoint operator. As in the flat case, all PTime computable queries over ordered databases are expressible in this language. The main result consists in proving that this language is a conservative extension of the first order logic with fixpoints, or of the while-queries (depending on the interpretation of the bounded fixpoint: inflationary or partial). The proof technique uses indexes, to encode complex objects into flat relations, and is strong enough to allow for the encoding of NRA with unbounded fixpoints into flat relations. We also define a logic based language with fixpoints, the nested relational calculus , and prove that its range restricted version is equivalent to NRA with bounded fixpoints
Proceedings of the Workshop on the lambda-Prolog Programming Language
The expressiveness of logic programs can be greatly increased over first-order Horn clauses through a stronger emphasis on logical connectives and by admitting various forms of higher-order quantification. The logic of hereditary Harrop formulas and the notion of uniform proof have been developed to provide a foundation for more expressive logic programming languages. The λ-Prolog language is actively being developed on top of these foundational considerations. The rich logical foundations of λ-Prolog provides it with declarative approaches to modular programming, hypothetical reasoning, higher-order programming, polymorphic typing, and meta-programming. These aspects of λ-Prolog have made it valuable as a higher-level language for the specification and implementation of programs in numerous areas, including natural language, automated reasoning, program transformation, and databases
Relational databases and homogeneity in logics with counting
We define a new hierarchy in the class of computable queries to relational databases, in terms of the preservation of equality of theories in fragments of first order logic with bounded number of variables with the addition of counting quantifiers (Ck). We prove that the hierarchy is strict, and it turns out that it is orthogonal to the TIME-SPACE hierarchy defined with respect to the Turing machine complexity. We introduce a model of computation of queries to characterize the different layers of our hierarchy which is based on the reflective relational machine of S. Abiteboul, C. Papadimitriou, and V. Vianu. In our model the databases are represented by their Ck theories. Then we define and study several properties of databases related to homogeneity in Ck getting various results on the change in the computation power of the introduced machine, when working on classes of databases with such properties. We study the relation between our hierarchy and a similar one which we defined in a previous work, in terms of the preservation of equality of theories in fragments of first order logic with bounded number of variables, but without counting quantifiers (FOk). Finally, we give a characterization of the layers of the two hierarchies in terms of the infinitary logics CK∞ω and LK∞ω respectively
- …