20,112 research outputs found
Language Constructs for Non-Well-Founded Computation
Recursive functions defined on a coalgebraic datatype C may not
converge if there are cycles in the input, that is, if the input object
is not well-founded. Even so, there is often a useful solution; for
example, the free variables of an infinitary λ-term, or the expected
running time of a finite-state probabilistic protocol.
Theoretical models of recursion schemes have been well studied
Extending the Calculus of Constructions with Tarski's fix-point theorem
We propose to use Tarski's least fixpoint theorem as a basis to define
recursive functions in the calculus of inductive constructions. This widens the
class of functions that can be modeled in type-theory based theorem proving
tool to potentially non-terminating functions. This is only possible if we
extend the logical framework by adding the axioms that correspond to classical
logic. We claim that the extended framework makes it possible to reason about
terminating and non-terminating computations and we show that common facilities
of the calculus of inductive construction, like program extraction can be
extended to also handle the new functions
Logic Programming Applications: What Are the Abstractions and Implementations?
This article presents an overview of applications of logic programming,
classifying them based on the abstractions and implementations of logic
languages that support the applications. The three key abstractions are join,
recursion, and constraint. Their essential implementations are for-loops, fixed
points, and backtracking, respectively. The corresponding kinds of applications
are database queries, inductive analysis, and combinatorial search,
respectively. We also discuss language extensions and programming paradigms,
summarize example application problems by application areas, and touch on
example systems that support variants of the abstractions with different
implementations
A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases
Ontologies and rules are usually loosely coupled in knowledge representation
formalisms. In fact, ontologies use open-world reasoning while the leading
semantics for rules use non-monotonic, closed-world reasoning. One exception is
the tightly-coupled framework of Minimal Knowledge and Negation as Failure
(MKNF), which allows statements about individuals to be jointly derived via
entailment from an ontology and inferences from rules. Nonetheless, the
practical usefulness of MKNF has not always been clear, although recent work
has formalized a general resolution-based method for querying MKNF when rules
are taken to have the well-founded semantics, and the ontology is modeled by a
general oracle. That work leaves open what algorithms should be used to relate
the entailments of the ontology and the inferences of rules. In this paper we
provide such algorithms, and describe the implementation of a query-driven
system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic)
rules under the well-founded semantics and a (monotonic) ontology, represented
by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic
Programming (TPLP
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