58,554 research outputs found
Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most
This paper proposes a way to compute the meanings associated with sentences
with generic noun phrases corresponding to the generalized quantifier most. We
call these generics specimens and they resemble stereotypes or prototypes in
lexical semantics. The meanings are viewed as logical formulae that can
thereafter be interpreted in your favourite models. To do so, we depart
significantly from the dominant Fregean view with a single untyped universe.
Indeed, our proposal adopts type theory with some hints from Hilbert
\epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval
philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears
some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et
al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to
classical examples involving a class, or a generic element of this class, which
is not uttered but provided by the context. An outcome of this study is that,
in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type
theoretical view, terms encode the purely semantic meaning component while
their typing is pragmatically determined
Analyzing Individual Proofs as the Basis of Interoperability between Proof Systems
We describe the first results of a project of analyzing in which theories
formal proofs can be ex- pressed. We use this analysis as the basis of
interoperability between proof systems.Comment: In Proceedings PxTP 2017, arXiv:1712.0089
A correspondence between rooted planar maps and normal planar lambda terms
A rooted planar map is a connected graph embedded in the 2-sphere, with one
edge marked and assigned an orientation. A term of the pure lambda calculus is
said to be linear if every variable is used exactly once, normal if it contains
no beta-redexes, and planar if it is linear and the use of variables moreover
follows a deterministic stack discipline. We begin by showing that the sequence
counting normal planar lambda terms by a natural notion of size coincides with
the sequence (originally computed by Tutte) counting rooted planar maps by
number of edges. Next, we explain how to apply the machinery of string diagrams
to derive a graphical language for normal planar lambda terms, extracted from
the semantics of linear lambda calculus in symmetric monoidal closed categories
equipped with a linear reflexive object or a linear reflexive pair. Finally,
our main result is a size-preserving bijection between rooted planar maps and
normal planar lambda terms, which we establish by explaining how Tutte
decomposition of rooted planar maps (into vertex maps, maps with an isthmic
root, and maps with a non-isthmic root) may be naturally replayed in linear
lambda calculus, as certain surgeries on the string diagrams of normal planar
lambda terms.Comment: Corrected title field in metadat
Probabilistic Operational Semantics for the Lambda Calculus
Probabilistic operational semantics for a nondeterministic extension of pure
lambda calculus is studied. In this semantics, a term evaluates to a (finite or
infinite) distribution of values. Small-step and big-step semantics are both
inductively and coinductively defined. Moreover, small-step and big-step
semantics are shown to produce identical outcomes, both in call-by- value and
in call-by-name. Plotkin's CPS translation is extended to accommodate the
choice operator and shown correct with respect to the operational semantics.
Finally, the expressive power of the obtained system is studied: the calculus
is shown to be sound and complete with respect to computable probability
distributions.Comment: 35 page
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