MATH 312H–FOUNDATIONS
... In order to make statements easily accessible we need to find a new language to express these statements in a simple form. In order to do this we introduce the following terminology: Often, a statement A depends on a variable, say t. This means that we are given a family of statements A(t) and A is ...
... In order to make statements easily accessible we need to find a new language to express these statements in a simple form. In order to do this we introduce the following terminology: Often, a statement A depends on a variable, say t. This means that we are given a family of statements A(t) and A is ...
2/TRUTH-FUNCTIONS
... s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement connectives: and, or, if...then, if and only if. When written in symbols they may be called logical oper ...
... s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement connectives: and, or, if...then, if and only if. When written in symbols they may be called logical oper ...
Lecture01 - Mathematics
... 1) Discrete mathematics a) Discrete mathematics is a catchall term that includes several branches of mathematics. The common thread is that these branches of mathematics typically have no use for the taking of limits (i.e.,the continuum mathematics of calculus, analysis, differential equations, topo ...
... 1) Discrete mathematics a) Discrete mathematics is a catchall term that includes several branches of mathematics. The common thread is that these branches of mathematics typically have no use for the taking of limits (i.e.,the continuum mathematics of calculus, analysis, differential equations, topo ...
Logic - Mathematical Institute SANU
... connectives and, or, if, if and only if and not, which are studied in propositional logic, and the quantifier expressions for every and for some, and identity (i.e. the relational expression equals), which, together with the connectives, are studied in predicate logic. If logic is indeed the theory ...
... connectives and, or, if, if and only if and not, which are studied in propositional logic, and the quantifier expressions for every and for some, and identity (i.e. the relational expression equals), which, together with the connectives, are studied in predicate logic. If logic is indeed the theory ...
Chapter 4. Logical Notions This chapter introduces various logical
... representing the form of m-formulas. Thus (p1Zp2) (viewed now as a metaformula) represents a form whose only instance is the formula (p1Zp2) itself, while (AZB) represents a form whose instances are all the disjunctive formulas. Of course, these formula instances will themselves have 'ordinary' sen ...
... representing the form of m-formulas. Thus (p1Zp2) (viewed now as a metaformula) represents a form whose only instance is the formula (p1Zp2) itself, while (AZB) represents a form whose instances are all the disjunctive formulas. Of course, these formula instances will themselves have 'ordinary' sen ...
Discrete Structure
... propositional logic that permits concisely reasoning about whole classes of entities. • Propositional logic (recall) treats simple propositions (sentences) as atomic entities. • In contrast, predicate logic distinguishes the subject of a sentence from its predicate. – Remember these English grammar ...
... propositional logic that permits concisely reasoning about whole classes of entities. • Propositional logic (recall) treats simple propositions (sentences) as atomic entities. • In contrast, predicate logic distinguishes the subject of a sentence from its predicate. – Remember these English grammar ...
INTERPLAYS OF KNOWLEDGE AND NON
... Considering this modal language with non-contingency operator ∆ meaning it is not contingent that and accepting a Hilbert-style presentation, the non-contingency logic S5∆ has the following set of axiom schemas (as defined in [11]): (A) ∆ϕ ↔ ∆¬ϕ; (B) ϕ → (∆(ϕ → ψ) → (∆ϕ → ∆ψ)); (C) ∆∆ϕ. It is usual ...
... Considering this modal language with non-contingency operator ∆ meaning it is not contingent that and accepting a Hilbert-style presentation, the non-contingency logic S5∆ has the following set of axiom schemas (as defined in [11]): (A) ∆ϕ ↔ ∆¬ϕ; (B) ϕ → (∆(ϕ → ψ) → (∆ϕ → ∆ψ)); (C) ∆∆ϕ. It is usual ...
071 Embeddings
... it stands because this disjunction gives the 0 of the lattice. We must treat each member of the list ...
... it stands because this disjunction gives the 0 of the lattice. We must treat each member of the list ...
Basic Metatheory for Propositional, Predicate, and Modal Logic
... whether every truth function is expressed by some formula of L P . The issue here hinges on the connectives of L P . A set of connectives in an interpreted language (i.e., a language together with its semantics) for propositional logic is said to be adequate iff every truth function can be expressed ...
... whether every truth function is expressed by some formula of L P . The issue here hinges on the connectives of L P . A set of connectives in an interpreted language (i.e., a language together with its semantics) for propositional logic is said to be adequate iff every truth function can be expressed ...
The Ring of Integers
... Elementary number theory is largely about the ring of integers, denoted by the symbol Z. The integers are an example of an algebraic structure called an integral domain. This means that Z satisfies the following axioms: (a) Z has operations + (addition) and · (multiplication). It is closed under the ...
... Elementary number theory is largely about the ring of integers, denoted by the symbol Z. The integers are an example of an algebraic structure called an integral domain. This means that Z satisfies the following axioms: (a) Z has operations + (addition) and · (multiplication). It is closed under the ...
