1,432 research outputs found
Evidence for Fixpoint Logic
For many modal logics, dedicated model checkers offer diagnostics (e.g., counterexamples) that help the user understand the result provided by the solver. Fixpoint logic offers a unifying framework in which such problems can be expressed and solved, but a drawback of this framework is that it lacks comprehensive diagnostics generation. We extend the framework with a notion of evidence, which can be specialized to obtain diagnostics for various model checking problems, behavioural equivalence and refinement checking problems. We demonstrate this by showing how our notion of evidence can be used to obtain diagnostics for the problem of deciding stuttering bisimilarity. Moreover, we show that our notion generalizes the existing notions of counterexample and witness for LTL and ACTL* model checking
A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics
Argumentation has proved a useful tool in defining formal semantics for
assumption-based reasoning by viewing a proof as a process in which proponents
and opponents attack each others arguments by undercuts (attack to an
argument's premise) and rebuts (attack to an argument's conclusion). In this
paper, we formulate a variety of notions of attack for extended logic programs
from combinations of undercuts and rebuts and define a general hierarchy of
argumentation semantics parameterised by the notions of attack chosen by
proponent and opponent. We prove the equivalence and subset relationships
between the semantics and examine some essential properties concerning
consistency and the coherence principle, which relates default negation and
explicit negation. Most significantly, we place existing semantics put forward
in the literature in our hierarchy and identify a particular argumentation
semantics for which we prove equivalence to the paraconsistent well-founded
semantics with explicit negation, WFSX. Finally, we present a general proof
theory, based on dialogue trees, and show that it is sound and complete with
respect to the argumentation semantics.Comment: To appear in Theory and Practice of Logic Programmin
A Potpourri of Reason Maintenance Methods
We present novel methods to compute changes to materialized
views in logic databases like those used by rule-based reasoners.
Such reasoners have to address the problem of changing axioms in the
presence of materializations of derived atoms. Existing approaches have
drawbacks: some require to generate and evaluate large transformed programs
that are in Datalog - while the source program is in Datalog and
significantly smaller; some recompute the whole extension of a predicate
even if only a small part of this extension is affected by the change.
The methods presented in this article overcome these drawbacks and derive
additional information useful also for explanation, at the price of an
adaptation of the semi-naive forward chaining
Characterising Probabilistic Processes Logically
In this paper we work on (bi)simulation semantics of processes that exhibit
both nondeterministic and probabilistic behaviour. We propose a probabilistic
extension of the modal mu-calculus and show how to derive characteristic
formulae for various simulation-like preorders over finite-state processes
without divergence. In addition, we show that even without the fixpoint
operators this probabilistic mu-calculus can be used to characterise these
behavioural relations in the sense that two states are equivalent if and only
if they satisfy the same set of formulae.Comment: 18 page
Reducing fuzzy answer set programming to model finding in fuzzy logics
In recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalisms allow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners
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