21,012 research outputs found
Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms
In this paper, we present two alternative approaches to defining answer sets
for logic programs with arbitrary types of abstract constraint atoms (c-atoms).
These approaches generalize the fixpoint-based and the level mapping based
answer set semantics of normal logic programs to the case of logic programs
with arbitrary types of c-atoms. The results are four different answer set
definitions which are equivalent when applied to normal logic programs. The
standard fixpoint-based semantics of logic programs is generalized in two
directions, called answer set by reduct and answer set by complement. These
definitions, which differ from each other in the treatment of
negation-as-failure (naf) atoms, make use of an immediate consequence operator
to perform answer set checking, whose definition relies on the notion of
conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other
two definitions, called strongly and weakly well-supported models, are
generalizations of the notion of well-supported models of normal logic programs
to the case of programs with c-atoms. As for the case of fixpoint-based
semantics, the difference between these two definitions is rooted in the
treatment of naf atoms. We prove that answer sets by reduct (resp. by
complement) are equivalent to weakly (resp. strongly) well-supported models of
a program, thus generalizing the theorem on the correspondence between stable
models and well-supported models of a normal logic program to the class of
programs with c-atoms. We show that the newly defined semantics coincide with
previously introduced semantics for logic programs with monotone c-atoms, and
they extend the original answer set semantics of normal logic programs. We also
study some properties of answer sets of programs with c-atoms, and relate our
definitions to several semantics for logic programs with aggregates presented
in the literature
Representing Conversations for Scalable Overhearing
Open distributed multi-agent systems are gaining interest in the academic
community and in industry. In such open settings, agents are often coordinated
using standardized agent conversation protocols. The representation of such
protocols (for analysis, validation, monitoring, etc) is an important aspect of
multi-agent applications. Recently, Petri nets have been shown to be an
interesting approach to such representation, and radically different approaches
using Petri nets have been proposed. However, their relative strengths and
weaknesses have not been examined. Moreover, their scalability and suitability
for different tasks have not been addressed. This paper addresses both these
challenges. First, we analyze existing Petri net representations in terms of
their scalability and appropriateness for overhearing, an important task in
monitoring open multi-agent systems. Then, building on the insights gained, we
introduce a novel representation using Colored Petri nets that explicitly
represent legal joint conversation states and messages. This representation
approach offers significant improvements in scalability and is particularly
suitable for overhearing. Furthermore, we show that this new representation
offers a comprehensive coverage of all conversation features of FIPA
conversation standards. We also present a procedure for transforming AUML
conversation protocol diagrams (a standard human-readable representation), to
our Colored Petri net representation
Relational Representations in Reinforcement Learning: Review and Open Problems
This paper is about representation in RL.We discuss some of the concepts in representation and generalization in reinforcement learning and argue for higher-order representations, instead of the commonly used propositional representations. The paper contains a small review of current reinforcement learning systems using higher-order representations, followed by a brief discussion. The paper ends with research directions and open problems.\u
On the strength of proof-irrelevant type theories
We present a type theory with some proof-irrelevance built into the
conversion rule. We argue that this feature is useful when type theory is used
as the logical formalism underlying a theorem prover. We also show a close
relation with the subset types of the theory of PVS. We show that in these
theories, because of the additional extentionality, the axiom of choice implies
the decidability of equality, that is, almost classical logic. Finally we
describe a simple set-theoretic semantics.Comment: 20 pages, Logical Methods in Computer Science, Long version of IJCAR
2006 pape
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