BCI-Algebras and Related Logics

Kabzinski in [6] first introduced an extension of BCI-logic that is isomorphic to BCI-algebras. Kashima and Komori in [7] gave a Gentzen-style sequent calculus version of this logic as well as another sequent calculus which they proved to be equivalent. They used the second to prove decidability of the word problem for BCI-algebras. The decidability proof relies on cut elimination for the second system, this paper provides a fuller and simpler proof of this. Also supplied is a new decidability proof and proof finding algorithm for their second extension of BCI-logic and so for BCI-algebras

The strong relevance logics

The tautology p - q - p is not a theorem of the various relevance logics (see Anderson and Belnap [1]) because q is not considered to be relevant in the derivation of final p. We can take this lack of relevance to mean simply that p-q-p could have been proved without q and its -, i.e., p-p. By the same criterion we could say that in ((p-p) -q) -q p-p is not relevant. In general we will say that any theorem A of an implicational logic is strongly relevant if there is no subpart B ! which can be removed from A, leaving the rest still a theorem of the same logic. Such a subpart B - is said to be superfluous

Child’s addition in the Stern–Brocot tree

AbstractWe use child’s addition and cross-differencing to discover significant relationships for diagonals, paths and branches within the Stern–Brocot tree and the Stern–Brocot sequence. This allows us to develop results for continued fraction summation under child’s addition

Intersection Type Systems and Logics Related to the Meyer–Routley System B+

Some, but not all, closed terms of the lambda calculus have types; these types are exactly the theorems of intuitionistic implicational logic. An extension of these simple (→) types to intersection (or →∧) types allows all closed lambda terms to have types. The corresponding →∧ logic, related to the Meyer–Routley minimal logic B+ (without ∨), is weaker than the →∧ fragment of intuitionistic logic. In this paper we provide an introduction to the above work and also determine the →∧ logics that correspond to certain interesting subsystems of the full →∧ type theory.&nbsp

Classical versions of BCI, BCK and BCIW logics

The question is, is there a formula X, independent of B,C,K1, I and W that creates distinct subclassical logics BCIX,BCKX and BCIWX, while BCKWX is the full classical implicational logic TV

Function Call Graph Score for Malware Detection

Metamorphic malware changes its internal structure with each infection, while maintaining its core functionality. Detecting such malware is a challenging research problem. Function call graph analysis has previously shown promise in detecting such malware. In this research, we analyze the robustness of a function call graph score with respect to various code morphing strategies. We also consider modifications of the score that make it more robust in the face of such morphing

On binary reflected Gray codes and functions

AbstractThe binary reflected Gray code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of m.This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder's result that the jth letter of the kth word of the binary reflected Gray code of length n is 2n-2n-j-1⌊2n-2n-j-1-k/2⌋mod2by replacing the binomial coefficient by k-12n-j+1+12

IgE Mediated Autoallergy against Thyroid Peroxidase – A Novel Pathomechanism of Chronic Spontaneous Urticaria?

Chronic spontaneous urticaria (csU), which is characterized by recurrent episodes of mast cell-driven wheal and flare-type skin reactions, is often associated with elevated total IgE levels and thyroid autoimmunity. We speculate that some csU patients express IgE autoantibodies against thyroid antigens such as thyroid peroxidase (TPO), which could bind to skin mast cells and induce their activation.We developed and used a site-directed human IgE capture ELISA to quantify IgE-anti-TPO. We used this assay and investigated csU patients (n = 478) and healthy control subjects (n = 127) for IgE-anti-TPO and then assessed IgE-anti-TPO-positive and -negative csU patients for clinical and serological differences. ( = 61%, IgE-anti-TPO: median 6.67, interquartile range 5.39–8.24). IgE-anti-TPO-positive and -negative csU patients had very similar distributions of age and gender as well as disease activity and duration. IgE-anti-TPO-positive csU patients exhibited significantly higher IgG-anti-TPO levels and lymphocyte counts as well as decreased C4 complement levels.Our findings show that a sizeable subgroup of csU patients expresses IgE antibodies against thyroid peroxidase. These autoantibodies could cause “autoallergic” mast cell activation, a novel pathomechanism of chronic spontaneous urticaria