We address the basic meaning of apparent contradictions of quantum theory and probability frameworks as expressed by Bell’s inequalities. We show that these contradictions have their origin in the incomplete considerations of the premisses of the derivation of the inequalities. A careful consideration of past work, including that of Boole and Vorob’ev, has lead us to the formulation of extended...

This paper is more a series of notes than a scholarly treatise. It focuses on certain achieve‐ ments of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed intending to broaden and to justify Aristotle’s, and giving a modern perspective to both logics. ...

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the model of Ivor Grattan-Guinness (1988 ), the tradition of the algebra of logic and the tradition of mathematical logic. They are represented by the developments going back to the British algebraist Georg...

– The theorem of Bell is a variant of Boole’s legendary consistency “conditions of possible experience.” Such an interpretation appears to be immune to arguments involving time dependencies put forward recently by Hess and Philipp [Europhysics Letters 57(6), 775-781, 2002], although experiments need not be. Boole’s “conditions of possible experience” and Pitowsky correlation polytopes. – In the...

Boole is a hash function designed by Gregory Rose and was submitted to the NIST Hash competition. It is a stream cipher based hash function which produces digests up to 512 bits. Different variants exist, namely Boole16, Boole32 and Boole64 where the number refers to word size in bits. Boole64 is considered as the official submission. In this paper we demonstrate a collision attack with complex...

Let us assume 0 6= ⋂ Ω (−ζω,W , . . . ,א0) → limx (e∅) · pi = { ∞ : k ( E, 1 ) ⊂ ∫ 1 −∞ lim infH (√ 2 ∩ α ) dρ } . It is well known that ι̃ = e. We show that every co-multiplicative, singular, anti-standard path is γ-globally one-to-one, n-dimensional and contra-associative. So it is not yet known whether r̄ is not larger than g, although [17, 17, 22] does address the issue of convexity. In futur...

In his influential Laws of Thought (1854), the mathematician George Boole presented a formulation of logic using algebraic expressions and manipulations. His widow, Mary Everest Boole, undertook an ambitious project of disseminating his ideas by introducing lay audiences to the law of pulsation, a prescription for correct reasoning that incorporates two of his fundamental insights. Contemporary...

We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases of a general approach to approximation. Herein we give details and extensions of this idea.

We propose new axiomatizations of the 24 assertoric syllogisms of Aristotle’s syllogistic, and the 2 n n-ary operations of Boole’s algebraic logic. The former organizes the syllogisms as a 6 × 4 table partitioned into four connected components according to which term if any must be inhabited. We give two natural-deduction style axiomatizations, one with four axioms and four rules, the second wi...