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Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

Data Analysis, Statistics and Probability · Physics 2011-09-12 Roberto C. Alamino

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

cmp-lg · Computer Science 2008-02-03 Rolf Backofen , Gert Smolka

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…

Logic in Computer Science · Computer Science 2015-07-01 Benjamin Werner

For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…

Algebraic Geometry · Mathematics 2026-02-16 Hyuk Jun Kweon

We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…

High Energy Physics - Theory · Physics 2016-10-12 Juan Pablo Babaro , Gaston Giribet , Arash Ranjbar

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative…

Algebraic Geometry · Mathematics 2008-05-29 R. Cluckers , F. Loeser

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

Algebraic Topology · Mathematics 2007-05-23 Martin Jakob

We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…

Mathematical Physics · Physics 2017-11-27 Wolfgang Bertram

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

Logic · Mathematics 2020-03-12 Lars Kristiansen , Juvenal Murwanashyaka

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…

Logic · Mathematics 2013-04-03 Fredrik Engström , Juha Kontinen , Jouko Väänänen

Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…

Logic in Computer Science · Computer Science 2026-03-20 Thomas Traversié , Florian Rabe

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…

High Energy Physics - Theory · Physics 2024-08-28 Clay Córdova , Daniel S. Freed , Constantin Teleman

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

History and Overview · Mathematics 2013-07-01 Felix Nagel

We present a formalization of convex polyhedra in the proof assistant Coq. The cornerstone of our work is a complete implementation of the simplex method, together with the proof of its correctness and termination. This allows us to define…

Logic in Computer Science · Computer Science 2018-08-14 Xavier Allamigeon , Ricardo D. Katz

Using the language of coarse homology theories, we provide an axiomatic account of vanishing results for the fibres of forget-control maps associated to spaces with equivariant finite decomposition complexity.

K-Theory and Homology · Mathematics 2019-10-30 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…

High Energy Physics - Theory · Physics 2011-03-18 A. V. Bratchikov

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.

Quantum Algebra · Mathematics 2007-05-23 Yael Fregier

We prove several combinatorial results on path algebras over discrete structures related to directed graphs. These results are motivated by Morse theory on a manifold with boundary and, more generally, by Floer theory on a configuration…

Geometric Topology · Mathematics 2013-01-01 Jonathan M. Bloom

The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…

Differential Geometry · Mathematics 2021-08-20 Matias del Hoyo , Mateus de Melo

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

Differential Geometry · Mathematics 2007-05-23 Mark Stern