A re-interpretation of the concept of mass and of the relativistic mass-energy relation

For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition - the so called mass-energy relation - aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the "rest-energy" of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10^9

Dual intuitionistic logic revisited

Abstract. We unify the algebraic, relational and sequent methods used by various authors to investigate “dual intuitionistic logic”. We show that restricting sequents to “singletons on the left/right ” cannot capture “intuitionistic logic with dual operators”, the natural hybrid logic that arises from intuitionistic and dual-intuitionistic logic. We show that a previously reported generalised display framework does deliver the required cut-free display calculus. We also pinpoint precisely the structural rule necessary to turn this display calculus into one for classical logic.

The Topology of Belief, Belief Revision and Defeasible Knowledge

We present a new topological semantics for doxastic logic, in which the belief modality is interpreted as the closure of the interior operator. We show that this semantics validates Stalnakerâ\u80\u99s epistemicdoxastic axioms [23], and indeed it is the most general (extensional) semantics validating them. We prove, among other things, that in this semantics the doxastic logic KD45 is sound and complete with respect to the class of all extremally disconnected topological spaces. We also give a topological semantics for conditional belief and show its connection to the operation of updating with â\u80\u9chard information â\u80\u9d (modeled by restricting the topology to a subspace). We show that our topological notions fit well with the defeasibility analysis of knowledge: topological knowledge coincides with undefeated true belief. We compare our semantics to the older topological interpretation of belief in terms of Cantor derivative (Steinsvold 2006), arguing in favor of our new semantics

On the computational complexity of spatial logics with connectedness constraints

We investigate the computational complexity of spatial logics extended with the means to represent topological connectedness and restrict the number of connected components. In particular, we show that the connectedness constraints can increase complexity from NP to PSpace, ExpTime and, if component counting is allowed, to NExpTime