118 research outputs found
Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics
We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer
and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We
give new analytic proof systems for A and use the embeddings to derive
corresponding systems for L. These include: hypersequent calculi for A and L
and terminating versions of these calculi; labelled single sequent calculi for
A and L of complexity co-NP; unlabelled single sequent calculi for A and L.Comment: 35 pages, 1 figur
Toward a probability theory for product logic: states, integral representation and reasoning
The aim of this paper is to extend probability theory from the classical to
the product t-norm fuzzy logic setting. More precisely, we axiomatize a
generalized notion of finitely additive probability for product logic formulas,
called state, and show that every state is the Lebesgue integral with respect
to a unique regular Borel probability measure. Furthermore, the relation
between states and measures is shown to be one-one. In addition, we study
geometrical properties of the convex set of states and show that extremal
states, i.e., the extremal points of the state space, are the same as the
truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal
logic for probabilistic reasoning on product logic events and prove soundness
and completeness with respect to probabilistic spaces, where the algebra is a
free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur
Tractable Query Answering and Optimization for Extensions of Weakly-Sticky Datalog+-
We consider a semantic class, weakly-chase-sticky (WChS), and a syntactic
subclass, jointly-weakly-sticky (JWS), of Datalog+- programs. Both extend that
of weakly-sticky (WS) programs, which appear in our applications to data
quality. For WChS programs we propose a practical, polynomial-time query
answering algorithm (QAA). We establish that the two classes are closed under
magic-sets rewritings. As a consequence, QAA can be applied to the optimized
programs. QAA takes as inputs the program (including the query) and semantic
information about the "finiteness" of predicate positions. For the syntactic
subclasses JWS and WS of WChS, this additional information is computable.Comment: To appear in Proc. Alberto Mendelzon WS on Foundations of Data
Management (AMW15
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