1,448 research outputs found
Generalized Veltman models with a root
Provability logic is a nonstandard modal logic. Interpretability logic is an extension of provability logic. Generalized Veltman models are Kripke like semantics for interpretability logic. We consider generalized
Veltman models with a root, i.e. r-validity, r-satisfiability and
a consequence relation. We modify Fine\u27s and Rautenberg\u27s proof
and prove non-compactness of interpretability logic
Lewis meets Brouwer: constructive strict implication
C. I. Lewis invented modern modal logic as a theory of "strict implication".
Over the classical propositional calculus one can as well work with the unary
box connective. Intuitionistically, however, the strict implication has greater
expressive power than the box and allows to make distinctions invisible in the
ordinary syntax. In particular, the logic determined by the most popular
semantics of intuitionistic K becomes a proper extension of the minimal normal
logic of the binary connective. Even an extension of this minimal logic with
the "strength" axiom, classically near-trivial, preserves the distinction
between the binary and the unary setting. In fact, this distinction and the
strong constructive strict implication itself has been also discovered by the
functional programming community in their study of "arrows" as contrasted with
"idioms". Our particular focus is on arithmetical interpretations of the
intuitionistic strict implication in terms of preservativity in extensions of
Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years
later
Embedded model discrepancy: A case study of Zika modeling
Mathematical models of epidemiological systems enable investigation of and
predictions about potential disease outbreaks. However, commonly used models
are often highly simplified representations of incredibly complex systems.
Because of these simplifications, the model output, of say new cases of a
disease over time, or when an epidemic will occur, may be inconsistent with
available data. In this case, we must improve the model, especially if we plan
to make decisions based on it that could affect human health and safety, but
direct improvements are often beyond our reach. In this work, we explore this
problem through a case study of the Zika outbreak in Brazil in 2016. We propose
an embedded discrepancy operator---a modification to the model equations that
requires modest information about the system and is calibrated by all relevant
data. We show that the new enriched model demonstrates greatly increased
consistency with real data. Moreover, the method is general enough to easily
apply to many other mathematical models in epidemiology.Comment: 9 pages, 7 figure
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