The predicate calculus then generalizes the "subject|predicate" form (where | symbolizes concatenation (stringing together) of symbols) into a form with the following blank-subject structure " _|predicate", and the predicate in turn generalized to all things with that property.Įxample: "This blue pig has wings" becomes two sentences in the propositional calculus: "This pig has wings" AND "This pig is blue", whose internal structure is not considered.
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" It breaks a simple sentence down into two parts (i) its subject (the object ( singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)). Relationship between propositional and predicate formulas
NOTION IF THEN FORMULA SERIES
"Dog!" probably implies "I see a dog" but should be rejected as too ambiguous.Įxample: "That purple dog is running", "This cow is blue", "Switch M31 is closed", "This cap is off", "Tomorrow is Friday".įor 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. 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. Thus the simple "primitive" assertions must be about specific objects or specific states of mind. "This cow is blue", "There's a coyote!" ("That coyote IS there, behind the rocks."). Simple propositions are declarative in nature, that is, they make assertions about the condition or nature of a particular object of sensation e.g. That horse is orange but this horse here is purple." is actually a compound proposition linked by "AND"s: ( ("This cow is blue" AND "that horse is orange") AND "this horse here is purple" ). A sequence of discrete sentences are considered to be linked by "AND"s, and formal analysis applies a recursive "parenthesis rule" with respect to sequences of simple propositions (see more below about well-formed formulas).įor example: The assertion: "This cow is blue. The linking semicolon " ", and connective "BUT" are considered to be expressions of "AND". Compound propositions are considered to be linked by sentential connectives, some of the most common of which are "AND", "OR", "IF.
If the values of all variables in a propositional formula are given, it determines a unique truth value. In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value.