2,610 research outputs found
Transformation-Based Bottom-Up Computation of the Well-Founded Model
We present a framework for expressing bottom-up algorithms to compute the
well-founded model of non-disjunctive logic programs. Our method is based on
the notion of conditional facts and elementary program transformations studied
by Brass and Dix for disjunctive programs. However, even if we restrict their
framework to nondisjunctive programs, their residual program can grow to
exponential size, whereas for function-free programs our program remainder is
always polynomial in the size of the extensional database (EDB).
We show that particular orderings of our transformations (we call them
strategies) correspond to well-known computational methods like the alternating
fixpoint approach, the well-founded magic sets method and the magic alternating
fixpoint procedure. However, due to the confluence of our calculi, we come up
with computations of the well-founded model that are provably better than these
methods.
In contrast to other approaches, our transformation method treats magic set
transformed programs correctly, i.e. it always computes a relevant part of the
well-founded model of the original program.Comment: 43 pages, 3 figure
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
The complexity of independence-friendly fixpoint logic
Abstract. We study the complexity of model-checking for the fixpoint extension of Hintikka and Sandu’s independence-friendly logic. We show that this logic captures ExpTime; and by embedding PFP, we show that its combined complexity is ExpSpace-hard, and moreover the logic includes second order logic (on finite structures).
Initial Draft of a Possible Declarative Semantics for the Language
This article introduces a preliminary declarative semantics for a subset of the language Xcerpt (so-called
grouping-stratifiable programs) in form of a classical (Tarski style) model theory, adapted to the specific
requirements of Xcerpt’s constructs (e.g. the various aspects of incompleteness in query terms, grouping
constructs in rule heads, etc.). Most importantly, the model theory uses term simulation as a replacement
for term equality to handle incomplete term specifications, and an extended notion of substitutions in
order to properly convey the semantics of grouping constructs. Based upon this model theory, a fixpoint
semantics is also described, leading to a first notion of forward chaining evaluation of Xcerpt program
An Effective Fixpoint Semantics for Linear Logic Programs
In this paper we investigate the theoretical foundation of a new bottom-up
semantics for linear logic programs, and more precisely for the fragment of
LinLog that consists of the language LO enriched with the constant 1. We use
constraints to symbolically and finitely represent possibly infinite
collections of provable goals. We define a fixpoint semantics based on a new
operator in the style of Tp working over constraints. An application of the
fixpoint operator can be computed algorithmically. As sufficient conditions for
termination, we show that the fixpoint computation is guaranteed to converge
for propositional LO. To our knowledge, this is the first attempt to define an
effective fixpoint semantics for linear logic programs. As an application of
our framework, we also present a formal investigation of the relations between
LO and Disjunctive Logic Programming. Using an approach based on abstract
interpretation, we show that DLP fixpoint semantics can be viewed as an
abstraction of our semantics for LO. We prove that the resulting abstraction is
correct and complete for an interesting class of LO programs encoding Petri
Nets.Comment: 39 pages, 5 figures. To appear in Theory and Practice of Logic
Programmin
Model-Checking Process Equivalences
Process equivalences are formal methods that relate programs and system
which, informally, behave in the same way. Since there is no unique notion of
what it means for two dynamic systems to display the same behaviour there are a
multitude of formal process equivalences, ranging from bisimulation to trace
equivalence, categorised in the linear-time branching-time spectrum.
We present a logical framework based on an expressive modal fixpoint logic
which is capable of defining many process equivalence relations: for each such
equivalence there is a fixed formula which is satisfied by a pair of processes
if and only if they are equivalent with respect to this relation. We explain
how to do model checking, even symbolically, for a significant fragment of this
logic that captures many process equivalences. This allows model checking
technology to be used for process equivalence checking. We show how partial
evaluation can be used to obtain decision procedures for process equivalences
from the generic model checking scheme.Comment: In Proceedings GandALF 2012, arXiv:1210.202
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