Gluing together proof environments: Canonical extensions of LF type theories featuring locks

© F. Honsell, L. Liquori, P. Maksimovic, I. Scagnetto This work is licensed under the Creative Commons Attribution License.We present two extensions of the LF Constructive Type Theory featuring monadic locks. A lock is a monadic type construct that captures the effect of an external call to an oracle. Such calls are the basic tool for gluing together diverse Type Theories and proof development environments. The oracle can be invoked either to check that a constraint holds or to provide a suitable witness. The systems are presented in the canonical style developed by the CMU School. The first system, CLLF/p,is the canonical version of the system LLF p, presented earlier by the authors. The second system, CLLF p?, features the possibility of invoking the oracle to obtain a witness satisfying a given constraint. We discuss encodings of Fitch-Prawitz Set theory, call-by-value λ-calculi, and systems of Light Linear Logic. Finally, we show how to use Fitch-Prawitz Set Theory to define a type system that types precisely the strongly normalizing terms

Dissociative identity disorder : features, etiology, and treatment

Dissociative Identity Disorder appears to be diagnosed more frequently in the current clinical arena. This may be connected to increased awareness of how people respond and cope with traumatic events, both singular and prolonged or serial. This increase in diagnoses may also correspond with new associations between childhood abuse and trauma, as well as research into how trauma is coded in memory. Dissociation can be viewed as a natural phenomena that, when overly utilized as a defense against trauma and its impact, may develop in some persons into DID. Treatment of DID tends to progress through four phases: initial, middle, preintegreation, and integration-postintegration. However, these stages frequently do not follow in order and may need to be revisited as the therapist and client encounter new parts in the client\u27s system. Accurate diagnosis, informed consent, and a strong therapeutic alliance that explicitly conveys trust and safety seem to be the most important elements in successful treatment of DID

π-calculus in (Co)inductive-type theory

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The Speed of Light and the Hubble Parameter: The Mass-Boom Effect

We prove here that Newtons universal gravitation and momentum conservation laws together reproduce Weinbergs relation. It is shown that the Hubble parameter H must be built in this relation, or equivalently the age of the Universe t. Using a wave-to-particle interaction technique we then prove that the speed of light c decreases with cosmological time, and that c is proportional to the Hubble parameter H. We see the expansion of the Universe as a local effect due to the LAB value of the speed of light co taken as constant. We present a generalized red shift law and find a predicted acceleration for photons that agrees well with the result from Pioneer 10/11 anomalous acceleration. We finally present a cosmological model coherent with the above results that we call the Mass-Boom. It has a linear increase of mass m with time as a result of the speed of light c linear decrease with time, and the conservation of momentum mc. We obtain the baryonic mass parameter equal to the curvature parameter, omega m = omega k, so that the model is of the type of the Einstein static, closed, finite, spherical, unlimited, with zero cosmological constant. This model is the cosmological view as seen by photons, neutrinos, tachyons etc. in contrast with the local view, the LAB reference. Neither dark matter nor dark energy is required by this model. With an initial constant speed of light during a short time we get inflation (an exponential expansion). This converts, during the inflation time, the Plancks fluctuation length of 10-33 cm to the present size of the Universe (about 1028 cm, constant from then on). Thereafter the Mass-Boom takes care to bring the initial values of the Universe (about 1015 gr) to the value at the present time of about 1055 gr.Comment: 15 pages, presented at the 9th Symposium on "Frontiers of Fundamental Physics", 7-9 Jan. 2008, University of Udine, Italy. Changed content

Quantum Information and Wave function Collapse

Inofrmation-theoretical restrictions on information transferred in the measurement of object S by information system O are studied. It is shown that such constraints, induced by Heisenberg commutation relations, result in the loss of information about the purity of S state. Consequently, it becomes impossible for O to discriminate pure and mixed S states. In individual events this effect is manifested by the stochastic outcomes of pure S state measurement, i.e. the collapse of pure S state.Comment: 8 pages, talk given on Simposium 'Frontiers of fundamental Physics', Udine, Italy, January 2008, to appear in Proceeding

Weak nuclear forces cause the strong nuclear force

We determine the strength of the weak nuclear force which holds the lattices of the elementary particles together. We also determine the strength of the strong nuclear force which emanates from the sides of the nuclear lattices. The strong force is the sum of the unsaturated weak forces at the surface of the nuclear lattices. The strong force is then about ten to the power of 6 times stronger than the weak force between two lattice points.Comment: 12 pages, 1 figur

Hidden-variable theory versus Copenhagen quantum mechanics

The main assumptions the Copenhagen quantum mechanics has been based on will be summarized and the known (not yet decided) contradiction between Einstein and Bohr will be newly analyzed. The given assumptions have been represented basically by time-dependent Schroedinger equation, to which some further assumptions have been added. Some critical comments have been raised against the given mathematical model structure by Pauli (1933) and by Susskind and Glogover (1964). They may be removed if only the Schroedinger equation is conserved and the additional assumptions are abandoned, as shown recently. It seems to be in contradiction to the numerous declarations that the Copenhagen model has been approved by experimental results. However, in the most of these experiments only the agreement with the mere Schroedinger equation has been tested. All mentioned assumptions have been tested practically only in the EPR experiment (measurement of coincidence light transmission through two polarizers) proposed originally by Einstein (1935). Also these experimental results have been interpreted as supporting the Copenhagen alternative, which has not been, however, true. In fact the microscopic world may be described correspondingly only with the help of the hidden-variable theory that is represented by the Schroedinger equation without mentioned additional assumptions, which has the consequence that the earlier interpretation gap between microscopic and macroscopic worlds has been removed. The only difference concerns the existence of discrete states. The possibilities of the human reason of getting to know the nature will be also shortly discussed in the beginning of this contribution.Comment: 10 pages, 2 figures; v2: local refinements and improvements of the tex

Properties of Set Functors

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A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles