. L O ] 1 9 A ug 2 00 3 GENERIC SUBSTITUTIONS
نویسنده
چکیده
Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from being a completed task. In manyvalued logic this dichotomy disappears: already in the finite-variable case many interesting phenomena occur, and the present paper aims at displaying some of these. 1. Preliminaries We work in the context of propositional algebraic logic. A continuous t-norm (tnorm for short) is a continuous function ⋆ from [0, 1] to [0, 1] such that ([0, 1], ⋆, 1) is a commutative monoid for which x ≤ y implies z ⋆ x ≤ z ⋆ y. Each t-norm induces a residuum → via x ≤ (y → z) iff x ⋆ y ≤ z. One checks easily that the usual lattice operations on [0, 1] are term-definable by x ∧ y = x ⋆ (x → y) and x ∨ y = (
منابع مشابه
ar X iv : 0 90 8 . 13 90 v 1 [ cs . L O ] 1 0 A ug 2 00 9 Nominal Abstraction
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompa...
متن کاملar X iv : 0 90 8 . 33 40 v 1 [ m at h . R T ] 2 3 A ug 2 00 9 DICHOTOMY FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF G
The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3 when p 6= 2. This ...
متن کاملar X iv : 0 90 8 . 33 40 v 2 [ m at h . R T ] 3 0 A ug 2 00 9 DICHOTOMY FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF G
The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3. This corresponden...
متن کاملnd - m at . s up r - co n ] 2 9 A ug 2 00 2 Direct Correlation between Tc and CuO 2 Bilayer Spacing in YBa 2 Cu 3 O 7 − x
متن کامل
ar X iv : m at h / 06 08 16 3 v 1 [ m at h . L O ] 7 A ug 2 00 6 IND - AND PRO - DEFINABLE SETS
We describe the indand procategories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005