77,287 research outputs found
Logic Conditionals, Supervenience, and Selection Tasks
Principles of cognitive economy would require that concepts about objects,
properties and relations should be introduced only if they simplify the
conceptualisation of a domain. Unexpectedly, classic logic conditionals,
specifying structures holding within elements of a formal conceptualisation, do
not always satisfy this crucial principle. The paper argues that this
requirement is captured by supervenience, hereby further identified as a
property necessary for compression. The resulting theory suggests an
alternative explanation of the empirical experiences observable in Wason's
selection tasks, associating human performance with conditionals on the ability
of dealing with compression, rather than with logic necessity
Towards a Convenient Category of Topological Domains
We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models
A Convenient Category of Domains
We motivate and define a category of "topological domains",
whose objects are certain topological spaces, generalising
the usual -continuous dcppos of domain theory.
Our category supports all the standard constructions of domain theory,
including the solution of recursive domain equations. It also
supports the construction of free algebras for (in)equational
theories, provides a model of parametric polymorphism,
and can be used as the basis for a theory of computability.
This answers a question of Gordon Plotkin, who asked
whether it was possible to construct a category of domains
combining such properties
Correspondence Truth and Quantum Mechanics
The logic of a physical theory reflects the structure of the propositions
referring to the behaviour of a physical system in the domain of the relevant
theory. It is argued in relation to classical mechanics that the propositional
structure of the theory allows truth-value assignment in conformity with the
traditional conception of a correspondence theory of truth. Every proposition
in classical mechanics is assigned a definite truth value, either 'true' or
'false', describing what is actually the case at a certain moment of time.
Truth-value assignment in quantum mechanics, however, differs; it is known, by
means of a variety of 'no go' theorems, that it is not possible to assign
definite truth values to all propositions pertaining to a quantum system
without generating a Kochen-Specker contradiction. In this respect, the
Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value
definiteness is consistently restored with respect to a determinate sublattice
of propositions defined by the state of the quantum system concerned and a
particular observable to be measured. An account of truth of contextual
correspondence is thereby provided that is appropriate to the quantum domain of
discourse. The conceptual implications of the resulting account are traced down
and analyzed at length. In this light, the traditional conception of
correspondence truth may be viewed as a species or as a limit case of the more
generic proposed scheme of contextual correspondence when the non-explicit
specification of a context of discourse poses no further consequences.Comment: 19 page
A Declarative Semantics for CLP with Qualification and Proximity
Uncertainty in Logic Programming has been investigated during the last
decades, dealing with various extensions of the classical LP paradigm and
different applications. Existing proposals rely on different approaches, such
as clause annotations based on uncertain truth values, qualification values as
a generalization of uncertain truth values, and unification based on proximity
relations. On the other hand, the CLP scheme has established itself as a
powerful extension of LP that supports efficient computation over specialized
domains while keeping a clean declarative semantics. In this paper we propose a
new scheme SQCLP designed as an extension of CLP that supports qualification
values and proximity relations. We show that several previous proposals can be
viewed as particular cases of the new scheme, obtained by partial
instantiation. We present a declarative semantics for SQCLP that is based on
observables, providing fixpoint and proof-theoretical characterizations of
least program models as well as an implementation-independent notion of goal
solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10
A Semantic Approach to the Completeness Problem in Quantum Mechanics
The old Bohr-Einstein debate about the completeness of quantum mechanics (QM)
was held on an ontological ground. The completeness problem becomes more
tractable, however, if it is preliminarily discussed from a semantic viewpoint.
Indeed every physical theory adopts, explicitly or not, a truth theory for its
observative language, in terms of which the notions of semantic objectivity and
semantic completeness of the physical theory can be introduced and inquired. In
particular, standard QM adopts a verificationist theory of truth that implies
its semantic nonobjectivity; moreover, we show in this paper that standard QM
is semantically complete, which matches Bohr's thesis. On the other hand, one
of the authors has provided a Semantic Realism (or SR) interpretation of QM
that adopts a Tarskian theory of truth as correspondence for the observative
language of QM (which was previously mantained to be impossible); according to
this interpretation QM is semantically objective, yet incomplete, which matches
EPR's thesis. Thus, standard QM and the SR interpretation of QM come to
opposite conclusions. These can be reconciled within an integrationist
perspective that interpretes non-Tarskian theories of truth as theories of
metalinguistic concepts different from truth.Comment: 19 pages. Further revision. Proof of Theorem 3.2.1 simplified,
Section 3.5 amended, minor changes in several sections. Accepted for
publication in Foundations of Physic
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