Propositional logic Flashcards
define a PL-wff
(i) Every sentence letter is a PL-wff
(ii) if π, π are wff then Β¬π, (πβπ), (πβ¨π), (πβ§π), and (πβοΈπ) are also PL-wffs
(iii) only what can be shown to be PL-wffs using (i) and (ii) are PL-wffs
When is a formula valid?
When the formula is true for all possible interpretations
When is an argument valid?
When the premises cannot be true and the conclusion false.
What is an informal proof?
A proof conducted in the natural language
What is a direct proof?
A proof that goes directly from the interpretations
What is an indirect proof?
A proof by contradiction that begins by assuming the contrary. (reductio ad absurdum).
When are two equations π and π semantically equivalent?
for all interpretations V(π)=V(π)
What is the natural deduction system?
The proof system that uses those long lines.
what does it mean to say that a language of propositional logic is βexpressively adequateβ?
it can express all truth-functions
Define completeness
A proof system is complete iff any valid formula and argument are provable in that system.
define logical consequence
certain claims logically follow from others - if the premises are true, then the conclusion is true
True or False:
A logically valid proposition is called a logical consequence
FALSE
a logically valid proposition is called a logical truth, a logically valid argument is called a logical consequence
define meta-language
The language used to describe the object language
what is a REFLEXIVE relation?
a has that relation to itself
what is a SYMMETRIC relation?
if a has R to b, then b has R to a
