After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard-Wiechert potentials of the particles are ev...

This paper describes a default reasoning problem, analogous to the frame problem, that arises when an attempt is made to construct a logic-based calculus for reasoning about the movement of objects in a real-valued co-ordinate system. A number of potential solutions to this problem are examined. Particular attention is given to the interaction between the default reasoning required by these sol...

(This paper is an extended abstract for an invited talk at 29th Linz Seminar on Fuzzy Set Theory, February 2008.) Höhle has shown that fuzzy sets, valued in a frame (complete Heyting algebra) Ω, can be identified with certain sheaves over Ω: they are the subsheaves of constant sheaves, and more general sheaves can be got as quotients of the fuzzy sets. The technical development is complicated b...

In the signal-processing literature, a frame is mechanism for performing analysis and reconstruction in Hilbert space. By contrast, quantum theory, positive operator-valued measure (POVM) decomposes Hilbert-space vector purpose of computing measurement probabilities. Frames their most common generalizations can be seen to give rise POVMs, but does every reasonable POVM arise from type frame? We...

The Brownian frame process T B is defined as T B t := (Bt−1+u)0≤u≤1 , t ∈ [0, 1] , where B is a real-valued Brownian motion with parameter set [−1, 1]. This thesis investigates properties of the path-valued Brownian frame process relevant to establishing an integration theory based on the theory of rough paths ([Lyons, 1998]). The interest in studying this object comes from its connection with ...

By interpreting ‘p is impossible’ by ‘p is selfcontradictory’, and ‘p is always’ by ‘not p is self-contradictory’, this paper studies which of the three-valued systems of Łucasiewicz, Gödel, Kleene, Bochvar, and Post, do verify the Aristotle’s principles of Non-Contradiction (NC), and Excluded-Middle (EM). Keywords— Systems of three-valued logic, Non-Contradiction, Excluded-Middle.

In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new binary sequent calculi (each sequent is a pair of formulae) for many valued logic with a finite set of truth values, and of Kripke-like semantics for it that is both sound and complete. We did not use the logic entailment based o...

In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

This paper presents an experiment with human subjects concerning the vague spatial relation ‘near’ in environmental space. After the topic is introduced and relevant previous work surveyed, the experiment is described. Three approaches to experimental analysis are presented and discussed: nearness neighbourhoods as regions with broad boundaries, fuzzy nearness and distance measures, and four-va...