14,979 research outputs found
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
Capturing k-ary Existential Second Order Logic with k-ary Inclusion-Exclusion Logic
In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is
obtained by extending first order logic with k-ary inclusion and exclusion
atoms. We show that every formula of INEX[k] can be expressed with a formula of
k-ary existential second order logic, ESO[k]. Conversely, every formula of
ESO[k] with at most k-ary free relation variables can be expressed with a
formula of INEX[k]. From this it follows that, on the level of sentences,
INEX[k] captures the expressive power of ESO[k].
We also introduce several useful operators that can be expressed in INEX[k].
In particular, we define inclusion and exclusion quantifiers and so-called term
value preserving disjunction which is essential for the proofs of the main
results in this paper. Furthermore, we present a novel method of relativization
for team semantics and analyze the duality of inclusion and exclusion atoms.Comment: Extended version of a paper published in Annals of Pure and Applied
Logic 169 (3), 177-21
An Ordinal View of Independence with Application to Plausible Reasoning
An ordinal view of independence is studied in the framework of possibility
theory. We investigate three possible definitions of dependence, of increasing
strength. One of them is the counterpart to the multiplication law in
probability theory, and the two others are based on the notion of conditional
possibility. These two have enough expressive power to support the whole
possibility theory, and a complete axiomatization is provided for the strongest
one. Moreover we show that weak independence is well-suited to the problems of
belief change and plausible reasoning, especially to address the problem of
blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in
Artificial Intelligence (UAI1994
GUBS, a Behavior-based Language for Open System Dedicated to Synthetic Biology
In this article, we propose a domain specific language, GUBS (Genomic Unified
Behavior Specification), dedicated to the behavioral specification of synthetic
biological devices, viewed as discrete open dynamical systems. GUBS is a
rule-based declarative language. By contrast to a closed system, a program is
always a partial description of the behavior of the system. The semantics of
the language accounts the existence of some hidden non-specified actions
possibly altering the behavior of the programmed device. The compilation
framework follows a scheme similar to automatic theorem proving, aiming at
improving synthetic biological design safety.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347
Guarded Teams: The Horizontally Guarded Case
Team semantics admits reasoning about large sets of data, modelled by sets of assignments (called teams), with first-order syntax. This leads to high expressive power and complexity, particularly in the presence of atomic dependency properties for such data sets. It is therefore interesting to explore fragments and variants of logic with team semantics that permit model-theoretic tools and algorithmic methods to control this explosion in expressive power and complexity.
We combine here the study of team semantics with the notion of guarded logics, which are well-understood in the case of classical Tarski semantics, and known to strike a good balance between expressive power and algorithmic manageability. In fact there are two strains of guardedness for teams. Horizontal guardedness requires the individual assignments of the team to be guarded in the usual sense of guarded logics. Vertical guardedness, on the other hand, posits an additional (or definable) hypergraph structure on relational structures in order to interpret a constraint on the component-wise variability of assignments within teams.
In this paper we investigate the horizontally guarded case. We study horizontally guarded logics for teams and appropriate notions of guarded team bisimulation. In particular, we establish characterisation theorems that relate invariance under guarded team bisimulation with guarded team logics, but also with logics under classical Tarski semantics
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