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Room P3.10, Mathematics Building
Jean-Yves Béziau, CNPq/FUNCAP - UFC, Fortaleza, Brazil
The first semantics for modal logic was put forward by Lukasiewicz. It was a three-valued semantics. Later on he proposed also a four-valued semantics. This approach to modal logic was dismissed due to: (1) the oddity of Lukasiewicz's systems (2) the result by Dugundji showing that S5 cannot be characterized by a finite matrix (3) the rise of Kripke semantics. I will show in this talk that: (a) we can built quite intuitive four-valued semantics for modal logic (b) it makes sense to develop modal logics based on finite matrices (c) the equation "modal logic = possible world semantics" is questionable.