Using the classification of formal deformation quantizations, and the formal, algebraic index theorem, I give a simple proof as to which formal deformation quantization (modulo isomorphism) is derived from a given geometric quantization.

A theorem of Pridham and Lurie provides an equivalence between formal moduli problems Lie algebras in characteristic zero. We prove a generalization this correspondence, relating parametrized by over Koszul operad to its dual operad. In particular, when the algebra associated deformation problem is induced from pre-Lie structure it corresponds permutative problem. As another example we obtain c...

We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation’s characterization of a hierarchy of pseudovarieties of finite lattices, progressively generalizing finite distributive lattices. This formal connection is mediated through monotone modal logic. Indeed, we adapt the correspondence algorithm ...

Formal knowledge modelling languages have a number of advantages over informal languages, such as their precise meaning and the possibility to derive properties through formal proofs. However, these formal languagesalso suffer from problems which limit their practical usefulness: they are often not expressive enough to deal with real world applications, formal models are complex and hard to rea...

belugais a proof environment that provides a rich sophisticated infrastructure for implementing formal systems based on the logical framework LF together with a first-order reasoning language for implementing inductive proofs about them following the Curry-Howard

We present a formal method for building proofs by analogy and its implementation as a proof tactic for the NuPRL proof development system. The Curry-Howard Isomorphism is used to represent proof constructions in a term-functional language and to specify analogies by transformation rules on these terms. The method has the advantage to admit complete formalization and to make use of well-known te...

We interpret walks in the first quadrant with steps {(1, 1), (1, 0), (−1, 0), (−1,−1)} as a generalization of Dyck words with two sets of letters. Using this language, we give a formal expression for the number of walks using the steps above, beginning and ending at the origin. We give an explicit formula for a restricted class of such words using a correspondence between such words and Dyck pa...

The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of research. Transformer-like semantics of internal definitions that combine a defining computation and an application will be presented. By specialisation for a g...

An attempt is made to apply a light cone dominance technique to the deep inelastic el ec troproduc tion of pions. A scaling law is derived which is in agreement with preliminary data. (Submitted to Physics Letters) * Work supported in part by the U. S. Atomic Energy Commission. t On leave of absence from the Department of Physics, Stanford University, Stanford, California 94305