Predicate Calculus Flashcards Preview

Logic > Predicate Calculus > Flashcards

Flashcards in Predicate Calculus Deck (7)
Loading flashcards...

What is special about 'predicate calculus' as opposed to other logic systems?

Have two new devices: Subject-predicate and quantifier-variable


Define a PC model

A PC model M is an ordered pair ⟨D, I⟩ such that:
D is a non-empty set (the domain)
I is a function (interpretation) such that:
- I(𝛼)∈D, where 𝛼 is a constant
- if Ξ  is a predicate then I(Ξ ) is a n-place relation over D


Define a PC-wff

(i) if Ξ  is a n-place predicate and 𝛼1, 𝛼2,..., 𝛼n, are terms, Π𝛼1𝛼2...𝛼n is a PC-wff
(ii) if πœ™, πœ“ are wff and 𝛼 is a variable then (πœ™β†’πœ“) and Β¬πœ™, etc and βˆƒπ›Όπœ™ and βˆ€π›Όπœ™ are also PC-wffs
(iii) only what can be shown to be PC-wffs using (i) and (ii) are PC-wffs


When is a variable bound?

when it is tied to a quantifier


What is an open formula? what is a closed formula?

A formula is open if it contains a free variable, closed otherwise


What is the scope of a quantifier?

For how much of the formula it applies.


define consistency and inconsistency

A formula is inconsistent if you can prove a contradiction from it. It is consistent if it is not inconsistent.