Related papers: Testing the equivalence principle: why and how?

First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…

We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…

Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

A policy maker faces a sequence of unknown outcomes. At each stage two (self-proclaimed) experts provide probabilistic forecasts on the outcome in the next stage. A comparison test is a protocol for the policy maker to (eventually) decide…

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…

We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…

Theory and empirical science should be in constant dialogue, but often find it hard to understand one another. Here we describe a graduate-level university course we developed to improve matters. The course was designed to help…

Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for…

In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice. We estimate all parameters, the strength of the objects and the boundaries of equal decision,…

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation,…

We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…

It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making…

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…

Empirical economic studies often involve multiple propositions or hypotheses, with researchers aiming to assess both the collective and individual evidence against these propositions or hypotheses. To rigorously assess this evidence,…

Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…

Process equivalences are formal methods that relate programs and system which, informally, behave in the same way. Since there is no unique notion of what it means for two dynamic systems to display the same behaviour there are a multitude…

This paper motivates the study of decision theory as necessary for aligning smarter-than-human artificial systems with human interests. We discuss the shortcomings of two standard formulations of decision theory, and demonstrate that they…