We introduce a simple translation from -calculus to combinatory logic (cl) such that: A is an sn -term i the translation result of A is an sn term of cl (the reductions are -reduction in -calculus and weak reduction in cl). None of the conventional translations from -calculus to cl satisfy the above property. Our translation provides a simpler sn proof of Godel's -calculus by the ordinal numbe...

The purpose of this note is to present a ternary propositional function which is a Sheffer function in the Heyting propositional calculus. We shall also consider some related Sheffer functions in positive logic. Although it is easy to guess what should be the general notion of a Sheffer function in a propositional calculus, we shall first fix our terminology. Following [2] and [1], we shall say...

We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony assumptions on the specification side and asynchronously interacting components in implementations. The join-calculus is promising to reduce this ...

In this paper we will write -[a 7→ -] as shorthand for (λa.-)-. Thus g[a 7→ h] stands for (λa.g)h and not for the term resulting from ‘substituting h for a in g’ (we write that as g[h/a], see Definition 44). The λ-calculus represents functions in programming languages [Pau96, Tho96], logic [Bar77, Lei94], theorem-provers [ABI96, Pau89], higher-order rewriting [BN98], and much more besides. Howe...

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

Building on a version of Lorenzen’s dialogue foundation for intuitionistic logic, we show that Gödel-Dummett logic G can be characterized by a suitable game of communicating parallel dialogues. This provides a computational interpretation of Avron’s hypersequent calculus for G.

The Kolmogorov and total variation distance between the laws of random variables have upper bounds represented by L1-norm densities when densities. In this paper, we derive an bound, in terms such as distance, for several probabilistic distances (e.g., Wasserstein Forter–Mourier etc.) F G case where a variable follows invariant measure that admits density differentiable G, sense Malliavin calcu...

Reddy 13] introduced an extended intuitionistic linear calculus to model some features of state-manipulation. His calculus LLMS { for Linear Logic Model of State { includes the connective \before" and an its associated modality y. De Paiva 5] presents a (collection of) dialectica categorical models for Classical Linear Logic, the categories GC. These categories contain an extra tensor product f...

Let $$G=(V,E)$$ be a locally finite graph. Firstly, using calculus of variations, including direct method variation and the mountain-pass theory, we get sequences solutions to several local equations on G (the Schrödinger equation, mean field Yamabe equation). Secondly, derive uniform estimates for those solution sequences. Finally, obtain global by extracting convergent sequence solutions. Our...

Background: Enterococci are important gram-positive bacteria causing dental calculus in human beings; however, the role of these bacteria in oral cavity is unclear. The aim of this study was to investigate the presence of Enterococcal Surface Protein (esp) gene in Enterococcus faecalis isolated from dental calculus in the city of Sari, Iran. Materials and Methods: In the present study, 207 den...