IV.3 Formal semantics of First Order Logic

Truth Table [Slide 118]

Again one could use truth tables to define the semantics of first order formulae but ...

Example 30.

Let A (A + 1 > A) be a formula

A
A + 1 > A
1
true
2
true

In order to determine the truth value of A (A + 1 > A) one needs to consider all rows in above truth table.

Truth tables are not suitable to determine the semantics or reason about first order formulae.

Semantics of formula [Slide 119]

We will use a denotational semantics to define the formal semantics of a first order formula.

Formulae ×State   Bool

State [Slide 120]

A State is the union of

State : (Vare   Val) (Varb   Bool)

where Vare Varb = .

We will use σ012,… to denote states and Σ to denote the set of all possible states.

Example 31.  

Let P be a Boolean variable and A be an integer variable then σ0 s.t. σ0(P) = tt and σ0(A) = 5 is a state.

2023-09-12
Contact | Home | ITL home | Course | Proofs | Algebra | FL
© 1996-2023