We propose a data structure for Boolean functions termed the Free Boolean Diagram. A Free Boolean Diagram allows decision vertices as in the conventional Binary Decision Diagram, but also allows function vertices corresponding to the and and xor functions. It has been shown previously that the equivalence of two Free Boolean Diagrams can be decided probabilistically in polynomial time. Based on...

Dempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (~, p), where S is a set of propositional clauses and p is an assignment of mass to each clause Ei c ~. It is shown that the disjunction of minimal support clauses for a clause...

We describe the Coalgebraic Ontology Logic solver COOL, a generic reasoner that decides the satisfiability of modal (and, more generally, hybrid) formulas with respect to a set of global assumptions – in Description Logic parlance, we support a general TBox and internalize a Boolean ABox. The level of generality is that of coalgebraic logic, a logical framework covering a wide range of modal lo...

Optimization can make at least two contributions to boolean logic. Its solution methods can address inference and satisfiability problems, and its style of analysis can reveal tractable classes of boolean problems that might otherwise have gone unnoticed. They key to linking optimization with logic is to provide logical formulas a numerical interpretation or semantics. While syntax concerns the...

We present the design and the implementation of clp(B): a boolean constraint solver in the Constraint Logic Programming paradigm. This solver is based on local propagation methods and follows the \glass-box" approach of compiling high-level constraints into primitive low-level ones. We detail its integration into the WAM showing that the necessary extension is truly minimal since only four new ...

The problem of computing the set prime implicants to represent a Boolean function is classical that still considered running for research because all known approaches have limitations. article reviews existing methods and highlights their limitations, particularly multi-output functions limited scalability due growth in memory required complete computation. Then it proposes recursive ternary-ba...

In this paper, we introduce and define Probabilistic Boolean Logic, whose logical operators are “correct” with a probability 0 < p ≤ 1. Analogous to conventional Boolean logic, we define well-formed probabilistic Boolean formulae (pbf). Every pbf is associated with two attributes, the underlying Boolean function it computes, and a for a specific input, the probability that this boolean function...

Abstract— The ability to control the transport of individual electrons in Single Electron Tunneling (SET) based circuits creates the conditions for Single Electron Encoded Logic (SEEL). The logic values and of SEEL gates are encoded as a net charge of or electron charges. This paper investigates the implementation of SEEL memory elements based on SEEL Boolean logic gates. After the introduction...

Background Fault tree analysis (FTA) is a well established method for qualitative as well as probabilistic reliability and safety analysis. Fault trees are Boolean models and thus do not support modelling of dynamic effects like sequence dependencies between fault events. In order to overcome this limitations, dynamic fault tree methods were defined previously. Most of these are based on comple...