474 research outputs found
A reconstruction of the multipreference closure
The paper describes a preferential approach for dealing with exceptions in
KLM preferential logics, based on the rational closure. It is well known that
the rational closure does not allow an independent handling of the inheritance
of different defeasible properties of concepts. Several solutions have been
proposed to face this problem and the lexicographic closure is the most notable
one. In this work, we consider an alternative closure construction, called the
Multi Preference closure (MP-closure), that has been first considered for
reasoning with exceptions in DLs. Here, we reconstruct the notion of MP-closure
in the propositional case and we show that it is a natural variant of Lehmann's
lexicographic closure. Abandoning Maximal Entropy (an alternative route already
considered but not explored by Lehmann) leads to a construction which exploits
a different lexicographic ordering w.r.t. the lexicographic closure, and
determines a preferential consequence relation rather than a rational
consequence relation. We show that, building on the MP-closure semantics,
rationality can be recovered, at least from the semantic point of view,
resulting in a rational consequence relation which is stronger than the
rational closure, but incomparable with the lexicographic closure. We also show
that the MP-closure is stronger than the Relevant Closure.Comment: 57 page
Precise Propagation of Upper and Lower Probability Bounds in System P
In this paper we consider the inference rules of System P in the framework of
coherent imprecise probabilistic assessments. Exploiting our algorithms, we
propagate the lower and upper probability bounds associated with the
conditional assertions of a given knowledge base, automatically obtaining the
precise probability bounds for the derived conclusions of the inference rules.
This allows a more flexible and realistic use of System P in default reasoning
and provides an exact illustration of the degradation of the inference rules
when interpreted in probabilistic terms. We also examine the disjunctive Weak
Rational Monotony of System P+ proposed by Adams in his extended probability
logic.Comment: 8 pages -8th Intl. Workshop on Non-Monotonic Reasoning NMR'2000,
April 9-11, Breckenridge, Colorad
On the KLM properties of a fuzzy DL with Typicality
The paper investigates the properties of a fuzzy logic of typicality. The
extension of fuzzy logic with a typicality operator was proposed in recent work
to define a fuzzy multipreference semantics for Multilayer Perceptrons, by
regarding the deep neural network as a conditional knowledge base. In this
paper, we study its properties. First, a monotonic extension of a fuzzy ALC
with typicality is considered (called ALC^FT) and a reformulation the KLM
properties of a preferential consequence relation for this logic is devised.
Most of the properties are satisfied, depending on the reformulation and on the
fuzzy combination functions considered. We then strengthen ALC^FT with a
closure construction by introducing a notion of faithful model of a weighted
knowledge base, which generalizes the notion of coherent model of a conditional
knowledge base previously introduced, and we study its properties.Comment: 15 page
Disjunctive antecedent conditionals
Disjunctive antecedent conditionals —conditionals of the form if A or B, C—sometimes seem to entail both of their simplifications and sometimes seem not to. I argue that this behavior reveals a genuine ambiguity in DACs. Along the way, I discuss a new observation about the role of focal stress in distinguishing the two interpretations of DACs. I propose a new theory, according to which the surface form of a DAC underdetermines its logical form: on one possible logical form, if A or B, C does entail both of its simplifications, while on the other, it does not
On Stalnaker's "Indicative Conditionals"
This paper is a guide to the main ideas and innovations in Robert Stalnaker's "Indicative Conditionals". The paper is for a volume of essays on twenty-one classics of formal semantics edited by Louise McNally and Zoltà n Gendler Szab
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