Related papers: Equality and equivalence, intuitionistically
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
We study a real valued propositional logic with unbounded positive and negative truth values that we call R-valued logic. Such logic slightly extends continuous propositional logic which, in turn, builds on Lukasiewicz many-valued logic.…
We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…
This paper is devoted to systematic studies of some extensions of first-order G\"odel logic. The first extension is the first-order rational G\"odel logic which is an extension of first-order G\"odel logic, enriched by countably many…
Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…
We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory
Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over…
We study first-order expansions of the reals which do not define the set of natural numbers. We also show that several stronger notions of tameness are equivalent to each others.
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions…
In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…
Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Goedel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but…
We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…