相关论文: A Naive Encoding of Russell's Paradox in Type Theo…

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…

Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…

Instantiation overflow is the property of those second order types for which all instances of full comprehension can be deduced from instances of atomic comprehension. In other words, a type has instantiation overflow when one can type, by…

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…

The intersection type assignment system has been designed directly as deductive system for assigning formulae of the implicative and conjunctive fragment of the intuitionistic logic to terms of lambda-calculus. But its relation with the…

Liouville type of theorems play a key role in the blow-up approach to study the global regularity of the three-dimensional Navier-Stokes equations. In this paper, we will prove Liouville type of theorems to the 3-D axisymmetric…

This short note introduces a formal system of truth and paradoxicality, outlining the main motivation, and proving its $\omega$-consistency. The system is called TP, for 'Truth and Paradoxicality'.

When we study the paradoxes of set theory we find out that there are mainly 2 types: the pathologies and the antinomies. These 2 notions are made precise and compared with the somehow inductively definable concept "abnormal". (See my paper…

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…

As one of the seven open problems in the addendum to their 1989 book "Computability in Analysis and Physics", Pour-El and Richards proposed ``... the recursion theoretic study of particular nonlinear problems of classical importance.…

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…

This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…

This paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of…

This paper investigates Voevodsky's univalence axiom in intensional Martin-L\"of type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various…

Denotational models of type theory, such as set-theoretic, domain-theoretic, or category-theoretic models use (actual) infinite sets of objects in one way or another. The potential infinite, seen as an extensible finite, requires a dynamic…

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing…

We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…

Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…

Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…