21,506 research outputs found
From Many-Valued Consequence to Many-Valued Connectives
Given a consequence relation in many-valued logic, what connectives can be
defined? For instance, does there always exist a conditional operator
internalizing the consequence relation, and which form should it take? In this
paper, we pose this question in a multi-premise multi-conclusion setting for
the class of so-called intersective mixed consequence relations, which extends
the class of Tarskian relations. Using computer-aided methods, we answer
extensively for 3-valued and 4-valued logics, focusing not only on conditional
operators, but on what we call Gentzen-regular connectives (including negation,
conjunction, and disjunction). For arbitrary N-valued logics, we state
necessary and sufficient conditions for the existence of such connectives in a
multi-premise multi-conclusion setting. The results show that mixed consequence
relations admit all classical connectives, and among them pure consequence
relations are those that admit no other Gentzen-regular connectives.
Conditionals can also be found for a broader class of intersective mixed
consequence relations, but with the exclusion of order-theoretic consequence
relations.Comment: Updated version [corrections of an incorrect claim in first version;
two bib entries added
A Social Pragmatic View on the Concept of Normative Consistency
The programmatic statement put forward in von Wright's last works on deontic logic introduces the perspective of logical pragmatics, which has been formally explicated here and extended so to include the role of norm-recipient as well as the role of norm-giver. Using the translation function from the language of deontic logic to the language of set-theoretical approach, the connection has been established between the deontic postulates, on one side, and the perfection properties of the norm-set and the counter-set, on the other side. In the study of conditions of rational norm-related activities it has been shown that diverse dynamic second-order norms related to the concept of the consistency norm-system hold: -- the norm-giver ought to restore ``classical'' consistency by revising an inconsistent system, -- the norm-recipient ought to preserve an inconsistent system by revision of its logic so that inconsistency does not imply destruction of the system.
Dialetheic deontic logic of Priest is a suitable logic for the purpose since it preserves other perfection properties of the system
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
A Proof-Theoretic Approach to Scope Ambiguity in Compositional Vector Space Models
We investigate the extent to which compositional vector space models can be
used to account for scope ambiguity in quantified sentences (of the form "Every
man loves some woman"). Such sentences containing two quantifiers introduce two
readings, a direct scope reading and an inverse scope reading. This ambiguity
has been treated in a vector space model using bialgebras by (Hedges and
Sadrzadeh, 2016) and (Sadrzadeh, 2016), though without an explanation of the
mechanism by which the ambiguity arises. We combine a polarised focussed
sequent calculus for the non-associative Lambek calculus NL, as described in
(Moortgat and Moot, 2011), with the vector based approach to quantifier scope
ambiguity. In particular, we establish a procedure for obtaining a vector space
model for quantifier scope ambiguity in a derivational way.Comment: This is a preprint of a paper to appear in: Journal of Language
Modelling, 201
Moduli spaces of rational weighted stable curves and tropical geometry
We study moduli spaces of rational weighted stable tropical curves, and their
connections with the classical Hassett spaces. Given a vector w of weights, the
moduli space of tropical w-stable curves can be given the structure of a
balanced fan if and only if w has only heavy and light entries. In this case,
we can express the moduli space as the Bergman fan of a graphic matroid.
Furthermore, we realize the tropical moduli space as a geometric
tropicalization, and as a Berkovich skeleton, of the classical moduli space.
This builds on previous work of Tevelev, Gibney--Maclagan, and
Abramovich--Caporaso--Payne. Finally, we construct the moduli spaces of
heavy/light weighted tropical curves as fiber products of unweighted spaces,
and explore parallels with the algebraic world.Comment: 26 pages, 8 TikZ figures. v3: Minor changes and corrections. Final
version to appear in Forum of Mathematics, Sigm
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