Proving Propositions

Wolfgang Schreiner
Research Institute for Symbolic Computation (RISC-Linz)
Johannes Kepler University, Linz, Austria

Overview

Motivation

Decomposition of Universally Quantified Formulas

Typical Constant Names

Example

Indirect Method for Universal Formulas

Decomposition of Existential Quantifications

Typical Use

Example

Indirect Method for Existential Formulas

Decomposition of Equivalences

Typical Use

Example

Decomposition of Implications

Example

Alternative

Indirect Method for Implications

Decomposition of Conjunctions

Example

Indirect Method for Conjunctions

Decomposition of Disjunctions

Explicitly Defined Predicates

Example

Explicitly Defined Functions

Example

Proof by Case Distinction

Example

Typical Use

Universal Quantification in Knowledge

Example

Existential Quantification in Knowledge

Example

Additional Knowledge

Infering Additional Knowledge

Propositional Consequences

Propositional Consequences (Continued)

Tautologies

Example

Quantifier Consequences

Quantifier Consequences (Continued)

Example

Substitutions

Summary

Author: Wolfgang Schreiner
Last Modification: November 30, 1999

[Up] [RISC-Linz] [University] [Search]