axioms

Derivation

Derivation is the process of establishing a result from a set of premises or axioms using logical rules. It's fundamental…

2 days ago

Theorem

A theorem is a statement proven true through logical deduction from accepted axioms and previously proven theorems. It forms a…

4 days ago

Syntactic Consequence in Formal Systems

Syntactic consequence defines the relationship between premises and conclusions derived through logical rules and axioms within a formal system. It…

4 days ago

Subtheory: Understanding Theories Within Theories

A subtheory is a specialized theory nested within a broader one. It shares some axioms and theorems but focuses on…

4 days ago

Soundness in Logic

Soundness ensures that a logical system's derived theorems are always true under any interpretation. It's a fundamental property for reliable…

4 days ago

Understanding Schema in Logic and Knowledge Representation

A schema is a template or pattern used in logic to represent a class of similar statements or propositions. It's…

4 days ago

Model in Logic and Mathematics

A model in logic and mathematics interprets the symbols of a formal language, satisfying the axioms and theorems of a…

4 days ago

Modal Operators in Logic

Modal operators like necessity (◻) and possibility (◊) alter a statement's truth value, indicating whether it must be true or…

4 days ago

Logical Theorem

A logical theorem is a statement proven true within a formal system. It relies on axioms and inference rules, representing…

4 days ago

Formal Proof Explained

A formal proof is a rigorous demonstration of truth within a formal system. Each step is precisely justified by a…

4 days ago