We define an action of the 0-Hecke algebra of type A on the Stanley-Reisner ring of the Boolean algebra. By studying this action we obtain a family of multivariate noncommutative symmetric functions, which specialize to the noncommutative Hall-Littlewood symmetric functions and their (q, t)-analogues introduced by Bergeron and Zabrocki. We also obtain multivariate quasisymmetric function identi...

The discussions which follow rest on a distinction, rust expounded by Husser!, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole...

The start of the computer revolution is considered to have taken place with the development of the ENIAC electronic digital computer in 1946, slightly more than 50 years ago, at the Moore School of Electrical Engineering at the University of Pennsylvania. I will trace the the scientiic developments that led to the ENIAC and other computers developed at around the same time. In antiquity, Euclid...

Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier inequalities presented by Boole and the findings of Vorob’ev as related to these inequalities. These findings together with a space-time generalization of Boole’s e...

Quantum value indefiniteness 1 refers to the impossibility of a consistent coexistence of certain complementary operationally incompatible quantum observables. It is inferred from three sources: i from quantum violations of constraints on classical probability distributions termed “conditions of possible experience” by Boole 2 , also known as the Boole-Bell-type inequalities 3 , ii from the Koc...

Rational analysis attempts to explain aspects of human cognition as an adaptive response to the environment (Marr, 1982; Anderson, 1990; Chater, Tenenbaum, & Yuille, 2006). The dominant approach to rational analysis today takes an ecologically reasonable specification of a problem facing an organism, given in statistical terms, then seeks an optimal solution, usually using Bayesian methods. Thi...

The foundation of an algebraic theory of binary relations was laid by C. S. Peirce, building on earlier work of Boole and De Morgan. The basic universe of discourse of this theory is a collection of binary relations over some set, and the basic operations on these relations are those of forming unions, complements, relative products (i.e., compositions), and converses (i.e., inverses). There is...

The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x : R → {0, 1} called states (R is the time set). If an asynchronous system is defined by making use of a so called generator function Φ : {0, 1} → {0, 1}, then it is called regular. The property of univers...

Peter Ladislaw Hammer was born in Timisoara, Romania, on December 23, 1936. He earned his Ph.D. in mathematics at the University of Bucharest in 1966. He defected to Israel in 1967 where he became a professor at the Technion in Haifa, and later moved to Canada, and taught at the University of Montreal (1969–1972), and at the University of Waterloo (1972–1983). In 1983, he moved to the USA and b...