# Category: Formal systems

Term graph
A term graph is a representation of an expression in a formal language as a generalized graph whose vertices are terms. Term graphs are a more powerful form of representation than expression trees bec
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίω
Proof (truth)
A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines,with both the nature of the evidence or justification and the cr
Axiom schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
Formal system
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are th
Rule of inference
In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion
Physical symbol system
A physical symbol system (also called a formal system) takes physical patterns (symbols), combining them into structures (expressions) and manipulating them (using processes) to produce new expression
Formal ethics
Formal ethics is a formal logical system for describing and evaluating the "form" as opposed to the "content" of ethical principles. Formal ethics was introduced by Harry J. Gensler, in part in his 19
Axiomatic system
In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-cont
First principle
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from First Cause a
Formal proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or fo
List of formal systems
This is a list of formal systems, also known as logical calculi.