In this paper we present a very general deduction theorem which -based upon a uniform notion of proof from hypotheses- holds for a very large class of logical systems. Most of the known results for classical and modal logics, as well as new results, are immediate corollaries of this theorem.
In this paper a semantical partition, relative to Kripke models, is introduced for sets of formulas. Secondly, this partition is used to generate a semantical hierarchy for modal formulas. In particular some results are given for the propositional calculi T and S4.
We present a design study based on a story-telling approach, to introduce multiplicative thinking at Kindergarten with an algebraic perspective. Starting from some theoretical assumptions about the use of narration in Math Education and about the psychological roots of multiplication, we build a suitable narrative context in order to promote children’s actions consistent with such roots.We analyse the development of this path and its management, emphasizing the special role played by the dialectics...
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