498 research outputs found
On a Straw Man in the Philosophy of Science - A Defense of the Received View
I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to make the concept of a theory more precise. Rather, it is meant as a generalizable framework for explicating specific theories
Kripke Models for Classical Logic
We introduce a notion of Kripke model for classical logic for which we
constructively prove soundness and cut-free completeness. We discuss the
novelty of the notion and its potential applications
Fully abstract models for effectful λ-calculi via category-theoretic logical relations
We present a construction which, under suitable assumptions, takes a model of Moggi’s computational λ-calculus with sum types, effect operations and primitives, and yields a model that is adequate and fully abstract. The construction, which uses the theory of fibrations, categorical glueing, ⊤⊤-lifting, and ⊤⊤-closure, takes inspiration from O’Hearn & Riecke’s fully abstract model for PCF. Our construction can be applied in the category of sets and functions, as well as the category of diffeological spaces and smooth maps and the category of quasi-Borel spaces, which have been studied as semantics for differentiable and probabilistic programming
Implicit complexity for coinductive data: a characterization of corecurrence
We propose a framework for reasoning about programs that manipulate
coinductive data as well as inductive data. Our approach is based on using
equational programs, which support a seamless combination of computation and
reasoning, and using productivity (fairness) as the fundamental assertion,
rather than bi-simulation. The latter is expressible in terms of the former. As
an application to this framework, we give an implicit characterization of
corecurrence: a function is definable using corecurrence iff its productivity
is provable using coinduction for formulas in which data-predicates do not
occur negatively. This is an analog, albeit in weaker form, of a
characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar
induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034
An inverse of the evaluation functional for typed Lambda-calculus
In any model of typed λ-calculus conianing some basic
arithmetic, a functional p - * (procedure—* expression)
will be defined which inverts the evaluation functional
for typed X-terms, Combined with the evaluation
functional, p-e yields an efficient normalization algorithm.
The method is extended to X-calculi with constants
and is used to normalize (the X-representations
of) natural deduction proofs of (higher order) arithmetic.
A consequence of theoretical interest is a strong
completeness theorem for βη-reduction, generalizing
results of Friedman [1] and Statman [31: If two Xterms
have the same value in some model containing
representations of the primitive recursive functions
(of level 1) then they are provably equal in the βη-
calculus
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