279 research outputs found
A graph-theoretic account of logics
A graph-theoretic account of logics is explored based on the general
notion of m-graph (that is, a graph where each edge can have a finite
sequence of nodes as source). Signatures, interpretation structures and
deduction systems are seen as m-graphs. After defining a category freely
generated by a m-graph, formulas and expressions in general can be seen
as morphisms. Moreover, derivations involving rule instantiation are also
morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different
logics encompassing, among others, substructural logics as well as logics
with nondeterministic semantics, and subsume all logics endowed with an
algebraic semantics
Weakly complete axiomatization of exogenous quantum propositional logic
A weakly complete finitary axiomatization for EQPL (exogenous quantum
propositional logic) is presented. The proof is carried out using a non trivial
extension of the Fagin-Halpern-Megiddo technique together with three Henkin
style completions.Comment: 28 page
Object certification
A brief overview is made of the use of temporal logic formalisms for
specifying and verifying concurrent systems in generar and information
systems in particular. The requirements imposed by object-orientation on
such formalisms are ·examined. A logic is proposed fulfilling those requirements
( except concerning non-monotonic features), allowing the uniform
treatment of both local and global properties of systems with concurrent,
interacting components organized in classes, and supporting specialization.
A semantics and a calculus (following an axiomatic, Hilbert style)
are presented in detail. The calculus includes rules for the sound inheritance
and reflection of theorems between classes. Practica! aspects of the
usage of such a logic for both specification and verification are considered.
To this end a set of metatheorems is provided for expediting the proof of
invariants. Finally, the need and availability of automatic theorem proving
for systems querying is briefly discussed
Time-stamped claim logic
The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. We introduce the Time-Stamped Claim Logic including a sound and complete sequent calculus. In order to show how Time-Stamped Claim Logic can be used in practice, we consider a concrete cyber-attribution case study
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