formal systems

Strong Kleene Connectives

Strong Kleene connectives are logical operators in three-valued logic designed by Stephen Cole Kleene. They handle indeterminate or undefined values,…

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

Simple Type Theory

Simple type theory organizes objects into a hierarchy of types, classes, and classes of classes. It contrasts with ramified type…

4 days ago

Understanding Signatures in Logic and Algebra

A signature in logic and algebra defines the set of symbols and their arities, specifying the operations, functions, and relations…

4 days ago

Sequent Calculus: A Formal System for Logical Deduction

Sequent calculus is a formal system representing logical deductions. It uses sequences of formulas before and after a turnstile, signifying…

4 days ago

Semi-Decidable Theory

A semi-decidable theory allows for an algorithm to list all its theorems. However, it may not offer a way to…

4 days ago

Semantically Closed Language

A semantically closed language includes its own truth predicate, enabling self-referential statements about the truth of sentences within the language…

4 days ago

Second-Order Logic Explained

Second-order logic enhances first-order logic by enabling quantification over predicates and relations, not just individuals. It offers greater expressive power…

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

Robinson Arithmetic

Robinson arithmetic is a simplified version of Peano arithmetic, omitting the induction axiom schema. It provides a weaker yet still…

4 days ago