Tõestussüsteemi

Tõestussüsteemi is a term used in logic and computer science that translates to "proof system" in English. It refers to a formal method for determining whether a given statement, often called a theorem or proposition, can be logically derived from a set of axioms or premises. A proof system establishes a set of rules of inference, which are a formalization of valid logical steps. When a statement can be reached from the axioms by applying these rules repeatedly, it is considered proven within that system.

The purpose of a proof system is to provide a rigorous and unambiguous way to establish the truth of mathematical or logical statements. Different proof systems exist, each with its own set of axioms and rules, suitable for different branches of logic or mathematics. For example, propositional logic proof systems deal with statements involving logical connectives like "and," "or," and "not," while predicate logic proof systems extend this to include quantifiers and variables.

In computer science, proof systems are fundamental to areas like automated theorem proving and formal verification. They allow computers to rigorously check the correctness of software and hardware designs by proving that they meet their specifications. The soundness of a proof system ensures that only true statements can be proven, while completeness ensures that all true statements within the system can be proven.