Counterexamples explain why a desired temporal logic property fails to hold, and as such are considered to be the most useful form of output from model-checkers. Multi-valued model-checking, introduced in [4] is an extension of classical model-checking. Instead of classical logic, it operates on elements of a given De Morgan algebra, e.g. the Kleene algebra [14]. Multi-valued modelchecking has ...

We study some boolean-like laws with iterative variables in Fuzzy Logic. We show that beyond the classical De Morgan triplets of connectives described by t-norms, t-conorms and strong negations there are interesting models with infinite solutions and surprising situations where there are none.

Visser’s rules form a basis for the admissible rules of IPC. Here we show that this result can be generalized to arbitrary intermediate logics: Visser’s rules form a basis for the admissible rules of any intermediate logic L for which they are admissible. This implies that if Visser’s rules are derivable for L then L has no non-derivable admissible rules. We also provide a necessary and suffici...

1 The setting, the purpose, and a warning Dov Gabbay is a prolific logician just by himself. But beyond that, he is quite good at making other people investigate the many further things he cares about. As a result, King’s College London has become a powerful attractor in our field worldwide. Thus, it is a great pleasure to be an organizer for one of its flagship events: the Augustus de Morgan W...

A. We prove Beurling's theorem and L p − L q Morgan's theorem for step two nilpotent Lie groups. These two theorems together imply a group of uncertainty theorems. 1. I Roughly speaking the Uncertainty Principle says that " A nonzero function f and its Fourier transform f cannot be sharply localized simultaneously ". There are several ways of measuring localization of a functi...

In this paper we show that an algebra Ω(m,n) is functionally free for the Berman class Km,n of Ockham algebras, that is, for any two polynomials f and g, they are identically equal in Km,n if and only if f = g holds in Ω(m,n). This result can be applied to the well-known algebras, e.g., Boolean, de Morgan, Kleene, Stone, Bunge algebras, and so on.

In this paper, the concept of extended intersection and restricted union of intuitionistic fuzzy soft sets are introduced. Some operations on intuitionistic fuzzy soft sets are investigated, and we prove that De Morgan’s laws hold in intuitionistic fuzzy soft sets theory. Based on these properties, we discuss the algebraic structures of intuitionistic fuzzy soft sets, which is lattice structure...

The monument to the work initiated by Boole, the algebraization of logic, is the three volumes Algebra der Logik by Schröder (1841–1902), which appeared in the years 1890–1910, filling over 2,000 pages. Although the spirit of the subject came from the work of Boole and De Morgan, Schröder's volumes are really a tribute to the work of C.S. Peirce, along with Schröder's contributions. In addition...

A small-biased function is a randomized function whose distribution of truth-tables is small-biased. We demonstrate that known explicit lower bounds on the size of (1) general Boolean formulas, (2) Boolean formulas of fan-in two, (3) de Morgan formulas, as well as (4) correlation lower bounds against small de Morgan formulas apply to small-biased functions. As a consequence, any strongly explic...

The authors would like to thank Aaron Blaisdell for the invitation to contribute to this special issue. We would also like to thank Rob Honey and Ulrike Hahn for their comments on previous versions of this manuscript. Correspondence should be addressed to Dr. D. M. Dwyer, School of Psychology, Cardiff University, Tower Building, Park Place, Cardiff, CF10 3AT, UK. ([email protected]). Ration...