logic

validity

if and only if it is necessary that if all its premises are true, its conclusion is true.

soundness

An argument is SOUND if and only if it is valid and all its premises are true.

tilde ~

“it is not the case that”, negation

ampersand &

“both”, “and”

Wedge V

“or”

arrow >

“if…. then”

double arrow <>

if and only if

expression

is any finite sequence of sentence letters, sentential connectives, or left and right parentheses.

WFF

(1) A sentence letter standing alone is a wff.

(2) If Φ is a wff, then the expression denoted by ∼Φ is also a wff.

(3) If Φ and Ψ are both wffs, then the expression denoted by (Φ & Ψ) is a wff.

(4) If Φ and Ψ are both wffs, then the expression denoted by (Φ ∨ Ψ) is a wff.

(5) If Φ and Ψ are both wffs, then the expression denoted by (Φ → Ψ) is a wff.

(6) If Φ and Ψ are both wffs, then the expression denoted by (Φ ↔ Ψ) is a wff.

(7) Nothing else is a wff.

atomic sentences

The sentence letters are the ATOMIC SENTENCES of the language of sentential logic. proposition

negation

a sentence where a tilde is present, showing that the premise is not the case

conjuction

a WFF where an & is present, connecting two wffs

disjunction

relation or connection of terms in a proposition to express the concept “or”; it is a statement of alternatives

conditional

first - antecedent

secondary - consequence

“if… then”

TT for conjunction

In order for a conjunction (Φ & Ψ) to be true, both conjuncts Φ and Ψ must be true

TT for disjunction

In order for a disjunction (Φ ∨ Ψ) to be false, both disjuncts Φ and Ψ must be false.

TT for conditional

In order for a conditional (Φ → Ψ) to be false, the antecedent Φ must be true while the consequent Ψ is false.

tt for biconditional

In order for a biconditional (Φ ↔ Ψ) to be true, both Φ and Ψ must have the same truth value.

tautology

when the sequent that has no premises and has Φ as its conclusion is valid.

inconsistent

A sentence that has only Fs under its column of a TT is INCONSISTENT.

contingent

Definition. A sentence that is neither tautologous nor inconsistent is CONTINGENT.