Category:Propositional logic (Aussagenlogik)
Overview
This page lists the most important terms and laws for the BFH module: Diskrete Mathematik I (BZG1155pa) 25/26
Propositional logic
Propositional logic (Aussagenlogik) is a formal system in logic that studies propositions and their relationships through logical connectives. It is the foundation of mathematical logic, computer science, and digital circuit design.
Propositions
A proposition (Aussage) is a declarative statement that is either true (wahr) or false (falsch), but not both.
Examples:
- "It is raining."
- "2 + 2 = 4."
- "The moon is made of cheese." (false, but still a proposition)
Syntax
Propositional formulas are built recursively:
- Every proposition symbol (p, q, r, …) is a formula.
- If φ is a formula, then ¬φ is a formula.
- If φ and ψ are formulas, then (φ ∧ ψ), (φ ∨ ψ), (φ → ψ), (φ ↔ ψ), … are formulas.
Semantics
The truth value of a formula is determined by the truth values of its components according to truth tables. This is called **truth-functional semantics**.
Terms
These are the basic logical connectives and symbols used in propositional logic.
- Negation (NOT)
- Conjunction (AND)
- Disjunction (OR)
- Implication (IF ... THEN)
- Equivalence (IF AND ONLY IF)
- Sheffer stroke (NAND)
See also
- Exclusive disjunction (XOR)
- Peirce arrow (NOR)
Logic Laws
These are the fundamental logical laws (Gesetze der Aussagenlogik) that are used to transform and simplify logical expressions.
Pages in category "Propositional logic (Aussagenlogik)"
The following 23 pages are in this category, out of 23 total.