Related papers: Identity of Proofs Based on Normalization and Gene…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate…

In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.

In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two…

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for…

Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…

This paper highlights three known identities, each of which involves sums over alternating sign matrices. While proofs of all three are known, the only known derivations are as corollaries of difficult results. The simplicity and natural…

Classically, two propositions are logically equivalent precisely when they are true under the same logical valuations. Also, two logical valuations are distinct if, and only if, there is a formula that is true according to one valuation,…

This paper is a survey of two kinds of "compressed" proof schemes, the \emph{matrix method} and \emph{proof nets}, as applied to a variety of logics ranging along the substructural hierarchy from classical all the way down to the…

Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…

Reproducibility, the ability to recompute results, and replicability, the chances other experimenters will achieve a consistent result, are two foundational characteristics of successful scientific research. Consistent findings from…

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a…

An identity by Ramanujan is expressed using polar coordinates, so that its proof reduces to the verification of an elementary trigonometric identity. This approach produces a few variations on Ramanujan's original identity.

In their recent book on combinatorial identities, Quaintance and Gould devoted one chapter to Melzak's identity. We give new proofs for this identity and its generalization.

Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…

A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a…

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…

Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…

Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…