9,276 research outputs found
Towards the implementation of a preference-and uncertain-aware solver using answer set programming
Logic programs with possibilistic ordered disjunction (or LPPODs) are a recently defined logic-programming framework based on logic programs with ordered disjunction and possibilistic logic. The framework inherits the properties of such formalisms and merging them, it supports a reasoning which is nonmonotonic, preference-and uncertain-aware. The LPPODs syntax allows to specify 1) preferences in a qualitative way, and 2) necessity values about the certainty of program clauses. As a result at semantic level, preferences and necessity values can be used to specify an order among program solutions. This class of program therefore fits well in the representation of decision problems where a best option has to be chosen taking into account both preferences and necessity measures about information. In this paper we study the computation and the complexity of the LPPODs semantics and we describe the algorithm for its implementation following on Answer Set Programming approach. We describe some decision scenarios where the solver can be used to choose the best solutions by checking whether an outcome is possibilistically preferred over another considering preferences and uncertainty at the same time.Postprint (published version
Answer Set Programming and Combinatorial Voting
We show how Logic Programming with Ordered
Disjunction (LPOD), the extension of answer
set programming for handling preferences, may
be used for representing and solving collective
decision making problems. We present the
notion of combinatorial vote problem in the
context of LPOD and define various types of
vote rules, used as decision criteria for
determining optimal candidate for a group of voters.
15 min presentatio
Characterizing and Extending Answer Set Semantics using Possibility Theory
Answer Set Programming (ASP) is a popular framework for modeling
combinatorial problems. However, ASP cannot easily be used for reasoning about
uncertain information. Possibilistic ASP (PASP) is an extension of ASP that
combines possibilistic logic and ASP. In PASP a weight is associated with each
rule, where this weight is interpreted as the certainty with which the
conclusion can be established when the body is known to hold. As such, it
allows us to model and reason about uncertain information in an intuitive way.
In this paper we present new semantics for PASP, in which rules are interpreted
as constraints on possibility distributions. Special models of these
constraints are then identified as possibilistic answer sets. In addition,
since ASP is a special case of PASP in which all the rules are entirely
certain, we obtain a new characterization of ASP in terms of constraints on
possibility distributions. This allows us to uncover a new form of disjunction,
called weak disjunction, that has not been previously considered in the
literature. In addition to introducing and motivating the semantics of weak
disjunction, we also pinpoint its computational complexity. In particular,
while the complexity of most reasoning tasks coincides with standard
disjunctive ASP, we find that brave reasoning for programs with weak
disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been
accepted for publication in Theory and Practice of Logic Programming,
Copyright Cambridge University Pres
Multirole Logic (Extended Abstract)
We identify multirole logic as a new form of logic in which
conjunction/disjunction is interpreted as an ultrafilter on the power set of
some underlying set (of roles) and the notion of negation is generalized to
endomorphisms on this underlying set. We formalize both multirole logic (MRL)
and linear multirole logic (LMRL) as natural generalizations of classical logic
(CL) and classical linear logic (CLL), respectively, and also present a
filter-based interpretation for intuitionism in multirole logic. Among various
meta-properties established for MRL and LMRL, we obtain one named multiparty
cut-elimination stating that every cut involving one or more sequents (as a
generalization of a (binary) cut involving exactly two sequents) can be
eliminated, thus extending the celebrated result of cut-elimination by Gentzen
From IF to BI: a tale of dependence and separation
We take a fresh look at the logics of informational dependence and
independence of Hintikka and Sandu and Vaananen, and their compositional
semantics due to Hodges. We show how Hodges' semantics can be seen as a special
case of a general construction, which provides a context for a useful
completeness theorem with respect to a wider class of models. We shed some new
light on each aspect of the logic. We show that the natural propositional logic
carried by the semantics is the logic of Bunched Implications due to Pym and
O'Hearn, which combines intuitionistic and multiplicative connectives. This
introduces several new connectives not previously considered in logics of
informational dependence, but which we show play a very natural role, most
notably intuitionistic implication. As regards the quantifiers, we show that
their interpretation in the Hodges semantics is forced, in that they are the
image under the general construction of the usual Tarski semantics; this
implies that they are adjoints to substitution, and hence uniquely determined.
As for the dependence predicate, we show that this is definable from a simpler
predicate, of constancy or dependence on nothing. This makes essential use of
the intuitionistic implication. The Armstrong axioms for functional dependence
are then recovered as a standard set of axioms for intuitionistic implication.
We also prove a full abstraction result in the style of Hodges, in which the
intuitionistic implication plays a very natural r\^ole.Comment: 28 pages, journal versio
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