A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of defining such sequent calculi for Pure Type Systems (PTS, which were originally presented in natural deduction style) and then organizing their rules for effective proof-search. We introduce the idea of Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the syntax of a permutation-free sequent calculus for propositional logic due to Herbelin, which is strongly related to natural deduction and already well adapted to proof-search. The operational semantics is adapted from Herbelin's and is defined by a system of local rewrite rules as in cut-elimination, using explicit substitutions. We prove confluence for this system. Restricting our attention to PTSC, a type system for the ground terms of this system, we obtain the Subject Reduction property and show that each PTSC is logically equivalent to its corresponding PTS, and the former is strongly normalising iff the latter is. We show how to make the logical rules of PTSC into a syntax-directed system PS for proof-search, by incorporating the conversion rules as in syntax-directed presentations of the PTS rules for type-checking. Finally, we consider how to use the explicitly scoped meta-variables of PTSCalpha to represent partial proof-terms, and use them to analyse interactive proof construction. This sets up a framework PE in which we are able to study proof-search strategies, type inhabitant enumeration and (higher-order) unification

Call-by-value non-determinism in a linear logic type discipline

We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard's second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction

Video Assisted Thoracoscopic Treatment of Pleuropericardial Cysts

Question of the Study In this study, safety and feasibility of thoracoscopic fenestration of pleuropericardial cysts under local and general anaesthesia is evaluated. Besides, a rare case of a pleural cyst, causing a superior vena cava syndrome, is described

Strong Zonation of Benthic Communities Across a Tidal Freshwater Height Gradient

Trade-offs associated with environmental gradients generate patterns of diversity and govern community organisation in a landscape. In freshwaters, benthic community structure is driven by trade-offs along generally orthogonal gradients of habitat permanence and predation—where ephemeral systems are physiologically harsh because of drying stress, but inhabitants are less likely to be under the intense predation pressure of more permanent waterbodies. However, in tidal freshwaters, these two stressors are compounding, and the trade-offs associated with them are decoupled. 2. We investigated benthic community structure in a tidal freshwater habitat. These communities experience a suite of conditions atypical for a freshwater habitat: twice-daily drying; and high predation pressure by mobile fishes. We compared benthic communities at three tidal heights (low, mid, high) and contrasted these with nearby non-tidal freshwaters that varied in their hydrology (permanent, temporary). 3. We found that communities were more strongly differentiated in tidal freshwater habitats than between permanent and temporary inland freshwaters, which was surprising given the high interconnectedness and condensed longitudinal scale of tidal habitats. The differentiation of communities in tidal habitats was probably driven by the combined gradients of desiccation risk at low tide and intense predation by fish at high tide—a combination of pressures that are novel for the evolutionary history of the regional freshwater invertebrate fauna. 4. Our study provides evidence that environmental gradients can produce stronger patterns of community zonation than would be predicted for habitats that are spatially contiguous and have little or no dispersal limitation. These results give insight into how communities might respond if drivers of community structure are altered or reorganised from their regional or evolutionary norms

Presupposition projection as proof construction

Even though Van der Sandt's presuppositions as anaphora approach is empirically successful, it fails to give a formal account of the interaction between world-knowledge and presuppositions. In this paper, an algorithm is sketched which is based on the idea of presuppositions as anaphora. It improves on this approach by employing a deductive system, Constructive Type Theory (CTT), to get a formal handle on the way world-knowledge influences presupposition projection. In CTT, proofs for expressions are explicitly represented as objects. These objects can be seen as a generalization of DRT's discourse markers. They are useful in dealing with presuppositional phenomena which require world-knowledge, such as Clark's bridging examples and Beaver's conditional presuppositions

The play's the thing

For very understandable reasons phenomenological approaches predominate in the field of sensory urbanism. This paper does not seek to add to that particular discourse. Rather it takes Rorty’s postmodernized Pragmatism as its starting point and develops a position on the role of multi-modal design representation in the design process as a means of admitting many voices and managing multidisciplinary collaboration. This paper will interrogate some of the concepts underpinning the Sensory Urbanism project to help define the scope of interest in multi-modal representations. It will then explore a range of techniques and approaches developed by artists and designers during the past fifty years or so and comment on how they might inform the question of multi-modal representation. In conclusion I will argue that we should develop a heterogeneous tool kit that adopts, adapts and re-invents existing methods because this will better serve our purposes during the exploratory phase(s) of any design project that deals with complexity

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

A Machine-Checked Formalization of the Generic Model and the Random Oracle Model

Most approaches to the formal analyses of cryptographic protocols make the perfect cryptography assumption, i.e. the hypothese that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. Ideally, one would prefer to rely on a weaker hypothesis on the computational cost of gaining information about the plaintext pertaining to a ciphertext without knowing the key. Such a view is permitted by the Generic Model and the Random Oracle Model which provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the proof assistant Coq, we provide a machine-checked account of the Generic Model and the Random Oracle Mode