14,099 research outputs found
Communicating answer set programs
Answer set programming i s a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mechanisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding communication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules
Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)
We produce a decidable classical normal modal logic of internalised
negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP)
from an existing logical counterpart of non-monotonic or instant interactive
proofs (LiiP). LDiiP internalises agent-centric proof theories that are
negation-complete (maximal) and consistent (and hence strictly weaker than, for
example, Peano Arithmetic) and enjoy the disjunction property (like
Intuitionistic Logic). In other words, internalised proof theories are
ultrafilters and all internalised proof goals are definite in the sense of
being either provable or disprovable to an agent by means of disjunctive
internalised proofs (thus also called epistemic deciders). Still, LDiiP itself
is classical (monotonic, non-constructive), negation-incomplete, and does not
have the disjunction property. The price to pay for the negation completeness
of our interactive proofs is their non-monotonicity and non-communality (for
singleton agent communities only). As a normal modal logic, LDiiP enjoys a
standard Kripke-semantics, which we justify by invoking the Axiom of Choice on
LiiP's and then construct in terms of a concrete oracle-computable function.
LDiiP's agent-centric internalised notion of proof can also be viewed as a
negation-complete disjunctive explicit refinement of standard KD45-belief, and
yields a disjunctive but negation-incomplete explicit refinement of
S4-provability.Comment: Expanded Introduction. Added Footnote 4. Corrected Corollary 3 and 4.
Continuation of arXiv:1208.184
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
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