This paper is concerned with providing a context based logic (language + semantics) for the representation of agents’s beliefs. While different approaches that make use of a single theory have been proposed in order to model agent’s beliefs, such as modal logics, these often suffer from problems, as lack of modularity, logical omniscence, and dissimilarity with implementations. A partial soluti...

In this chapter, a new rotation-invariant generalization of the analytic signal will be presented to analyze intrinsic 1D and 2D local image structures. By combining differential geometry and Clifford analysis, the monogenic curvature tensor can be derived to perform a split of identity and to enable simultaneous estimation of local amplitude, phase, main orientation and angle of intersection i...

In the signal theory framework the "analytic signal” is a particular polar representation of a signal . It defines an envelope (a modulus) and a phase (an argument) and these parameters are basic in communications. In this paper, we show that amplitude demodulations generally change envelopes and reduced phases. Consequently we show that recent results in laser communications about these parame...

In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tree-like tableaux of size n are counted by n!, and which moreover respects most of the well-known statistics studied originally o...

The paper provides a recipe for adequately representing a very inclusive class of finite-valued logics by way of tableaux. The only requisite for applying the method is that the object logic received as input should be sufficiently expressive, in having the appropriate linguistic resources that allow for a bivalent representation. For each logic, the tableau system obtained as output has some a...

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The appr...

In [11,13] we showed how to combine propositional BDI logics using Gabbay’s fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based decision procedure for the combined/fibred logics. We show how to uniformly construct a tableau calculus for the combined logic using Governatori’s labelled tableau system KEM.

An axiomatic formulation of a logic called LPS4 appears in [3]. Here that logic is proved sound and complete with respect to the weak semantics of [7]. Also a tableau system for LPS4 is introduced, and also proved sound and complete with respect to the semantics, thus establishing both cut elimination and equivalence with the axiomatic formulation.

We implement an algorithm for extracting appropriate collections of classiclike sound and complete tableau rules for a large class of finite-valued logics. Its output consists of Isabelle theories.

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G0-system of Terng...