24,808 research outputs found
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
Decoherence, the measurement problem, and interpretations of quantum mechanics
Environment-induced decoherence and superselection have been a subject of
intensive research over the past two decades, yet their implications for the
foundational problems of quantum mechanics, most notably the quantum
measurement problem, have remained a matter of great controversy. This paper is
intended to clarify key features of the decoherence program, including its more
recent results, and to investigate their application and consequences in the
context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio
Refinement by interpretation in {\pi}-institutions
The paper discusses the role of interpretations, understood as multifunctions
that preserve and reflect logical consequence, as refinement witnesses in the
general setting of pi-institutions. This leads to a smooth generalization of
the refinement-by-interpretation approach, recently introduced by the authors
in more specific contexts. As a second, yet related contribution a basis is
provided to build up a refinement calculus of structured specifications in and
across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348
Post Completeness in Congruential Modal Logics
Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is truth-functional. As Humberstone notes, the issue of Post completeness in congruential modal logics is not well understood. The present article shows that in contrast to normal modal logics, the extent of the property of Post completeness among congruential modal logics depends on the background set of logics. Some basic results on the corresponding properties of Post completeness are established, in particular that although a congruential modal logic is Post complete among all modal logics if and only if its modality is truth-functional, there are continuum many modal logics Post complete among congruential modal logics
On past participle agreement in transitive clauses in French
This paper provides a Minimalist analysis of past participle agreement in French in transitive
clauses. Our account posits that the head v of vP in such structures carries an (accusativeassigning) structural case feature which may apply (with or without concomitant agreement)
to case-mark a clause-mate object, the subject of a defective complement clause, or an
intermediate copy of a preposed subject in spec-CP. In structures where a goal is extracted
from vP (e.g. via wh-movement) v also carries an edge feature, and may also carry a
specificity feature and a set of (number and gender) agreement features. We show how these
assumptions account for agreement of a participle with a preposed specific clausemate object
or defective-clause subject, and for the absence of agreement with an embedded object, with
the complement of an impersonal verb, and with the subject of an embedded (finite or nonfinite) CP complement. We also argue that the absence of agreement marking (in expected
contexts) on the participles faitmade and laissélet in infinitive structures is essentially viral in
nature. Finally, we claim that obligatory participle agreement with reflexive and reciprocal
objects arises because the derivation of reflexives involves A-movement and concomitant
agreement
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