Download Logica Universalis: Towards a General Theory of Logic by Jean-Yves Beziau PDF
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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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 }.