MATH20302 Propositional Logic
... such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). The definition above is an inductive one, with (0) being the base case an ...
... such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). The definition above is an inductive one, with (0) being the base case an ...
Sample pages 2 PDF
... Therefore, ¬A ⇒ B ∧ C ⇔ D effectively means ((¬A) ⇒ (B ∧ C)) ⇔ D. Although we can reduce brackets to a minimum, we usually use brackets to distinguish between ∧ and ∨, and between ⇒ and ⇔. Therefore, we would usually write A ∨ (B ∧ C) even if A ∨ B ∧ C would do. Similarly, we write A ⇔ (B ⇒ C) when ...
... Therefore, ¬A ⇒ B ∧ C ⇔ D effectively means ((¬A) ⇒ (B ∧ C)) ⇔ D. Although we can reduce brackets to a minimum, we usually use brackets to distinguish between ∧ and ∨, and between ⇒ and ⇔. Therefore, we would usually write A ∨ (B ∧ C) even if A ∨ B ∧ C would do. Similarly, we write A ⇔ (B ⇒ C) when ...
Introduction to Linear Logic - Shane Steinert
... the category defined as follows: Objects are pairs (X , Y ) with X ∈ C and Y ∈ D. Morphisms in hom((X , Y ), (X 0 , Y 0 )) are a pair (f , g ) with f ∈ hom(X , X 0 ) and g ∈ hom(Y , Y 0 ). Composition is componentwise: ...
... the category defined as follows: Objects are pairs (X , Y ) with X ∈ C and Y ∈ D. Morphisms in hom((X , Y ), (X 0 , Y 0 )) are a pair (f , g ) with f ∈ hom(X , X 0 ) and g ∈ hom(Y , Y 0 ). Composition is componentwise: ...
1. Propositional Logic 1.1. Basic Definitions. Definition 1.1. The
... “cut-free”), which consists of the rules of Pc other than Cut, and prove cutelimination—that every proof in Pc can be converted to one in Pcf c —and speed-up—that there are sequences which have short deductions in Pc , but have only very long deductions in Pcf c . Among other things, this will tell ...
... “cut-free”), which consists of the rules of Pc other than Cut, and prove cutelimination—that every proof in Pc can be converted to one in Pcf c —and speed-up—that there are sequences which have short deductions in Pc , but have only very long deductions in Pcf c . Among other things, this will tell ...
Modal fixpoint logic: some model theoretic questions
... MSO is an extension of first-order logic, which allows quantification over subsets of the domain. It is also one of the most expressive logics that is known to be decidable on trees, whether they are binary or unranked (that is, there is no restriction on the number a successors of a node). Hence, i ...
... MSO is an extension of first-order logic, which allows quantification over subsets of the domain. It is also one of the most expressive logics that is known to be decidable on trees, whether they are binary or unranked (that is, there is no restriction on the number a successors of a node). Hence, i ...
Problems on Discrete Mathematics1
... We use Dx , Dy to denote the domains of x and y, respectively. Note that Dx and Dy do not have to be the same. In the above example, P (3, 2) is the proposition 3 ≥ 22 with truth value F . Similarly, Q(Boo, dog) is a proposition with truth value T if there is a dog named Boo. Note: Any proposition i ...
... We use Dx , Dy to denote the domains of x and y, respectively. Note that Dx and Dy do not have to be the same. In the above example, P (3, 2) is the proposition 3 ≥ 22 with truth value F . Similarly, Q(Boo, dog) is a proposition with truth value T if there is a dog named Boo. Note: Any proposition i ...
