By Jean-Yves Beziau

Universal common sense isn't really a brand new common sense, yet a normal conception of logics, regarded as mathematical buildings. The identify used to be brought approximately ten years in the past, however the topic is as previous because the starting of recent good judgment. It used to be revived after the flowering of millions of latest logics over the past thirty years: there has been a necessity for a scientific concept of logics to place a few order during this chaotic multiplicity.
The current ebook includes contemporary works on common common sense by way of top notch researchers from all over the international. The booklet is stuffed with new and tough rules that would advisor the way forward for this interesting topic. will probably be of curiosity for those that are looking to higher comprehend what good judgment is. it is going to support people who are misplaced within the jungle of heterogeneous logical platforms to discover a manner. instruments and ideas are supplied right here if you are looking to research periods of already current logics or are looking to layout and construct new ones.

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To appear. [35] Saharon Shelah and Jouko V¨ aa ¨n¨ anen. Recursive logic frames. Mathematical Logic Quarterly, to appear. [36] C. I. Steinhorn. Borel structures and measure and category logics. In Model-theoretic logics, Perspect. Math. Logic, pages 579–596. Springer, New York, 1985. [37] Leslie H. Tharp. The characterization of monadic logic. J. Symb. , 38(3):481–488, 1973. [38] Jouko V¨ aa ¨n¨ anen. Pseudo-finite model theory. Mat. , 24:169–183, 2003. 8th Workshop on Logic, Language, Informations and Computation—WoLLIC’2001 (Bras´ılia).

Theoria, 35:1–11, 1969. [23] Steven Orey. On ω-consistency and related properties. J. Symb. Logic, 21:246–252, 1956. [24] R. Parikh and J. V¨ aa ¨n¨ anen. Finite information logic. Annals of Pure and Applied Logic. to appear. [25] E. L. Post. Introduction to a general theory of elementary propositions. American Journal Mathematics, 43:163 – 185, 1921. Abstract Model Theory as a Framework for Universal Logic 33 [26] Maarten de Rijke. A Lindstr¨ om’s theorem for modal logic. In Modal Logic and Process Algebra, Lecture Notes 53, pages 217–230.

G is L-surjective, if for any [a ]L ∈ (ExprL =L ) there is some expression a ∈ ExprL such that g(a) ∈ [a ]L . The function f (the function g) is L-bijective, if it is L-injective and L surjective, respectively. f is regular, if for all A, B ∈ IntL holds: A =L B =⇒ f (A) =L f (B). g is regular, if for all a, b ∈ ExprL holds: a =L b =⇒ g(a) =L g(b). (ii) A logic-homomorphism from L to L is a pair (f, g) of continuous functions f : IntL → IntL and g : ExprL → ExprL . More precisely, the pair (f, g) is a logic-homomorphism, if for every a ∈ ExprL there exists an Aa ⊆ ExprL such that the following holds: • f −1 (M odL (a )) = {(M odL (a)) | a ∈ Aa } and • g −1 (a ∗L ) = {a∗L | a ∈ Aa }.

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