Propositional Formula - Propositions

For the purposes of the propositional calculus, propositions (utterances, sentences, assertions) are considered to be either simple or compound. Compound propositions are considered to be linked by sentential connectives, some of the most common of which are AND, OR, "IF ... THEN ...", "NEITHER ... NOR...", "... IS EQUIVALENT TO ..." . The linking semicolon " ; ", and connective BUT are considered to be expressions of AND. A sequence of discrete sentences are considered to be linked by ANDs, and formal analysis applies a recursive "parenthesis rule" with respect to sequences of simple propositions (see more below about well-formed formulas).

For example: The assertion: "This cow is blue. That horse is orange but this horse here is purple." is actually a compound proposition linked by ANDs: " ( ("This cow is blue" AND "that horse is orange") AND "this horse here is purple" ) ".

Simple propositions are declarative in nature, that is, they make assertions about the condition or nature of a particular object of sensation e.g. "This cow is blue", "There's a coyote!" ("That coyote IS there, behind the rocks."). Thus the simple "primitive" assertions must be about specific objects or specific states of mind. Each must have at least a subject (an immediate object of thought or observation), a verb (in the active voice and present tense preferred), and perhaps an adjective or adverb. "Dog!" probably implies "I see a dog" but should be rejected as too ambiguous.

Example: "That purple dog is running", "This cow is blue", "Switch M31 is closed", "This cap is off", "Tomorrow is Friday".

For the purposes of the propositional calculus a compound proposition can usually be reworded into a series of simple sentences, although the result will probably sound stilted.