We start from the geometrical-logical extension of Aristotle's square in [6,15] and [14], and study them from both syntactic and semantic points of view. Recall that Aristotle's square under its modal form has the following four vertices: A is α, E is ¬α, I is ¬ ¬α and O is ¬ α, where α is a logical formula and is a modality which can be defined axiomatically within a particular logic known as S5 (classical or intuitionistic, depending on whether ¬ is involutive or not) modal logic.[3] has proposed extensions which can be interpreted respectively within paraconsistent and paracomplete logical frameworks.[15] has shown that these extensions are subfigures of a tetraicosahedron whose vertices are actually obtained by closure of {α, α} by the logical operations {¬, ∧, ∨}, under the assumption of classical S5 modal logic. We pursue these researches on the geometrical-logical extensions of Aristotle's square: first we list all modal squares of opposition. We show that if the vertices of that geometrical figure are logical formulae and if the sub-alternation edges are interpreted as logical implication relations, then the underlying logic is none other than classical logic. Then we consider a higher-order extension introduced by [14], and we show that the same tetraicosahedron plays a key role when additional modal operators are introduced. Finally we discuss the relation between the logic underlying these extensions and the resulting geometrical-logical figures.
Abstract. Systems engineering deals with artificial systems conceived by human beings. These systems are combinations of elements aiming at one or more definite goals. Sociotechnical systems consist in technical parts, concerning systems engineering issues, and in human and organizational parts, concerning medical and social sciences issues. Resilience reports to the capacity of sociotechnical systems to adjust faced with disturbing events, to adapt and learn the adequate rules of adaptation, when the disturbances are out of the specified perimeter of the system's adaptation mechanisms. After having characterized resilience, the article highlights its relevance to the field of the sociotechnical systems. Then, sociotechnical systems' resilience is articulated with systems engineering and architecture in order to evolve systems engineering processes, engineering models, system architecture and enabling systems. Lastly, the article underlines the fact that systems engineering is necessary and owes being supplemented of good practices of management which contribute to the of sociotechnical systems resilience.
The paper attempts to give a formal framework to capture the entire process of scientific discovery including hypothesis formation, reasoning, identifying contradictions, peer reviewing, reformulating and so on. Data mining can be seen as one step in this complex process of interactive learning of an empirical theory This paper uses the terminology from paraconsistent logic and paracomplete logic that extends Aristotle square in a hypercube of oppositions which defines or substantiates any step of the discovery process. The central formal notions are validated on a mathematical scientific discovery game, and an industrial application in the field of Drug Discovery illustrates how the presented framework combines different learning processes to predict pharmaco-kinetic properties (ADME-T) and adverse side effects of therapeutic drug molecules.
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