In classical Boolean logic, data is represented as being either entirely true or entirely false. In most real world phenomena however, it is rare that en entity will be absolutely true or absolutely false. When designing a system, Boolean logic lacks the tools necessary to deal with this kind of uncertainty. Using fuzzy logic we were able to develop a system that is able to deal with uncertaint...

The logic of bunched implications (BI) of O’Hearn and Pym [5] is a substructural logic which freely combines additive connectives ⊃ , ∧, ∨ from propositional logic and multiplicative connectives −?, ? from linear logic. Because of its concise yet rich representation of states of resources, BI is regarded as a logic suitable for reasoning about resources. For example, by building a model for BI ...

Finding solution values for unknowns in Boolean equations was, along with second-order quantifier elimination, a principal reasoning mode in the Algebra of Logic of the 19th century. Schröder [19] investigated it as Auflösungsproblem (solution problem). It is closely related to the modern notion of Boolean unification. For a given formula that contains unknowns formulas are sought such that aft...

Static function hierarchies and models of the dynamic behaviour are typically used in e-commerce systems. Issues to be verifies are the completeness and correctness of the static function hierarchies, business rules valid in defined business domains and the consistency of models on different levels of abstraction. Today the systems are mostly tested manually. Automated support may the verificat...

A new class of connectionist architectures is presented called ASOCS (Adaptive Self-Organizing Concurrent Systems) [3,4]. ASOCS models support efficient computation through self-organized learning and parallel execution. Learning is done through the incremental presentation of rules and/or examples. Data types include Boolean and multi-state variables; recent models support analog variables. Th...

The Facebook discussion with Stephen King about Stone spaces led to a highly interesting development of ideas concerning Boolean, algebras, Stone spaces, and p-adic physics. I have discussed these ideas already earlier but the improved understanding of the notion of Stone space helped to make the ideas more concrete. The basic ideas are briefly summarized. p-adic integers/numbers correspond to ...

Optimization algorithms used in binary multi-level logic synthesis, such as network simplification, logic extraction, and resubstitution, have been treated independently and did not share computational procedures. Using multi-valued logic synthesis, some common conceptual and computational cores underlying these algorithms can be identified. We present an overview of a Boolean paradigm in multi...

Rapid single flux quantum (RSFQ) logic needs synchronous pulses for each gate, so the clock-wiring problem is more serious when designing larger scale circuits with this logic. So we have proposed a new SFQ logic which follows Boolean algebra perfectly by using set and reset pulses. With this logic, the level information of current input is transmitted with these pulses generated by level-to-pu...

Probability is usually closely related to Boolean structures, i.e. Boolean algebras or propositional logic. Here we show, how probability can be combined with Non-Boolean structures, and in particular Non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenar...

In the field of Business Process Management formal models for the control flow of business processes have been designed since more than 15 years. Which methods are best suited to verify the bulk of these models? The first step is to select a formal language which fixes the semantics of the models. We adopt the language of Boolean systems as reference language for Boolean process models. Boolean...