Characterization of quantum states in predicative logic

We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of random first order domain and find a characterization of pure states in predicative logic and mixed states in propositional logic, due to a focusing condition. We discuss the role of first order variables and the related contextuality, in terms of sequents.Comment: 14 pages, Boston, IQSA10, to appea

A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

TA treatment of depression: a hermeneutic single-case efficacy design study- 'Penelope'

This study is the second of a series of three, and represents an Italian replication of a previous UK -based case series (Widdowson 2012a, 2012b, 2012c, 2013) that investigated the effectiveness of a recently manualised transactional analysis treatment for depression with British clients, using Hermeneutic Single-Case Efficacy Design (HSCED). The various stages of HSCED as a systematic case study research method are described, as a quasi-judicial method to sift case evidence in which researchers construct opposing arguments around multiple sources of quantitative and qualitative evidence and judges evaluate these to conclude whether the client changed substantially over the course of therapy, and whether the outcome was attributable to the therapy. The therapist in this case was a white Italian man in the third year of training to become a psychotherapist, and the client, Penelope, was a 45- year old white Italian woman with mild depression and anxiety. The conclusion of the judges was that this was a mixed-outcome case: the client improved some aspects of her problems, without obtaining a complete and stable remission. Interestingly, this case presents a minimal correlation between empirical and proxy-rated indexes of depression and anxiety and answers to self reported questionnaires, raising the question of validity of self report measures with specific typology of client

Dualities for modal algebras from the point of view of triples

In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by Cartesian product on the relational side and show that in some cases the corresponding operation on the algebraic side represents bimorphisms

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

Collection Principles in Dependent Type Theory

We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation in- terpretation

Emergence of qualia from brain activity or from an interaction of proto-consciousness with the brain: which one is the weirder? Available evidence and a research agenda

This contribution to the science of consciousness aims at comparing how two different theories can explain the emergence of different qualia experiences, meta-awareness, meta-cognition, the placebo effect, out-of-body experiences, cognitive therapy and meditation-induced brain changes, etc. The first theory postulates that qualia experiences derive from specific neural patterns, the second one, that qualia experiences derive from the interaction of a proto-consciousness with the brain\u2019s neural activity. From this comparison it will be possible to judge which one seems to better explain the different qualia experiences and to offer a more promising research agenda

北海道における知的障がい者の就労支援に関する一考察

知的障がい者の就労について、北海道及び北海道教育委員会が進めている障が いのある人の就労支援の充実に向けた取組の状況を概観することに加えて、北海道内 の特別支援学校在籍者の約８割を占めている知的障がい特別支援学校の現状や就労支 援の取組について整理した。北海道において障がいある人の就労に大きな役割を果た してきた職親会の設立の経緯やなよろ地方職親会の障がい者雇用の状況やジョブコー チ養成研修の成果をまとめた。以上のことを踏まえて、知的障がい者の就労支援やキ ャリア教育の在り方について考察する