16,515 research outputs found
Epistemic Foundation of Stable Model Semantics
Stable model semantics has become a very popular approach for the management
of negation in logic programming. This approach relies mainly on the closed
world assumption to complete the available knowledge and its formulation has
its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and
epistemic-based characterization of stable model semantics, to the
Gelfond-Lifschitz transformation. In particular, we show that stable model
semantics can be defined entirely as an extension of the Kripke-Kleene
semantics. Indeed, we show that the closed world assumption can be seen as an
additional source of `falsehood' to be added cumulatively to the Kripke-Kleene
semantics. Our approach is purely algebraic and can abstract from the
particular formalism of choice as it is based on monotone operators (under the
knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming
(TPLP
Super Logic Programs
The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful
nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper,
we specialize it to a class of theories called `super logic programs'. We argue
that these programs form a natural generalization of standard logic programs.
In particular, they allow disjunctions and default negation of arbibrary
positive objective formulas.
Our main results are two new and powerful characterizations of the static
semant ics of these programs, one syntactic, and one model-theoretic. The
syntactic fixed point characterization is much simpler than the fixed point
construction of the static semantics for arbitrary AELB theories. The
model-theoretic characterization via Kripke models allows one to construct
finite representations of the inherently infinite static expansions.
Both characterizations can be used as the basis of algorithms for query
answering under the static semantics. We describe a query-answering interpreter
for super programs which we developed based on the model-theoretic
characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200
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
On Berry's conjectures about the stable order in PCF
PCF is a sequential simply typed lambda calculus language. There is a unique
order-extensional fully abstract cpo model of PCF, built up from equivalence
classes of terms. In 1979, G\'erard Berry defined the stable order in this
model and proved that the extensional and the stable order together form a
bicpo. He made the following two conjectures: 1) "Extensional and stable order
form not only a bicpo, but a bidomain." We refute this conjecture by showing
that the stable order is not bounded complete, already for finitary PCF of
second-order types. 2) "The stable order of the model has the syntactic order
as its image: If a is less than b in the stable order of the model, for finite
a and b, then there are normal form terms A and B with the semantics a, resp.
b, such that A is less than B in the syntactic order." We give counter-examples
to this conjecture, again in finitary PCF of second-order types, and also
refute an improved conjecture: There seems to be no simple syntactic
characterization of the stable order. But we show that Berry's conjecture is
true for unary PCF. For the preliminaries, we explain the basic fully abstract
semantics of PCF in the general setting of (not-necessarily complete) partial
order models (f-models.) And we restrict the syntax to "game terms", with a
graphical representation.Comment: submitted to LMCS, 39 pages, 23 pstricks/pst-tree figures, main
changes for this version: 4.1: proof of game term theorem corrected, 7.: the
improved chain conjecture is made precise, more references adde
Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism
We give extensional and intensional characterizations of nondeterministic
functional programs: as structure preserving functions between biorders, and as
nondeterministic sequential algorithms on ordered concrete data structures
which compute them. A fundamental result establishes that the extensional and
intensional representations of non-deterministic programs are equivalent, by
showing how to construct a unique sequential algorithm which computes a given
monotone and stable function, and describing the conditions on sequential
algorithms which correspond to continuity with respect to each order.
We illustrate by defining may and must-testing denotational semantics for a
sequential functional language with bounded and unbounded choice operators. We
prove that these are computationally adequate, despite the non-continuity of
the must-testing semantics of unbounded nondeterminism. In the bounded case, we
prove that our continuous models are fully abstract with respect to may and
must-testing by identifying a simple universal type, which may also form the
basis for models of the untyped lambda-calculus. In the unbounded case we
observe that our model contains computable functions which are not denoted by
terms, by identifying a further "weak continuity" property of the definable
elements, and use this to establish that it is not fully abstract
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