SE212 - Predicate Logic

In predicate logic, symbols can represent more interesting values like the “flight level of A” and we can use ”<” as a symbol over numbers with its standard meaning

Compared to propositional logic the only possible semantic values for symbols are T and F

• Predicates (relations) - Allows us to describe the attributes/properties of values or relationships between 2 or more values
  • Eg. “Billy is a child”, “Billy” is the value and Being a “child” is an attribute of Billy
• Unary Predicate - Predicate that takes a single argument
• Binary Predicate - Predicate that takes 2 arguments
  • and so on, it’s called n-nary predicate
• UNTYPED Predicate Logic - Symbols are categorized as either functions or predicates, there’s no notion of what kind of value a function returns
• Type Environment - Set of basic types and types for all the constants and functions in the formula
• Type Inference - process of figuring out a type environment types for functions, constants, and types for variables that make a formula a wff
• ^d Notation
  • ^d where d is an element of the universe in the middle of a formula within […] means “in this spot was a variable that has the value d”
  • ^d should only appear with […]

Transformational Proof §

Natural Deduction §

• Variable Capture - location in the formula that had a free variables before substitution, has a term containing a bound variables after the substitution
• Genuine Variable - Free variable such that the universal quantification of it yields a formula that is true, represents any value
• Unknown Variable - Free variable such that the existential quantification of it yields a formula that is true

Semantic Tableaux §