Boethius’ Theses
Boethius' theses are two formulas in propositional logic: (A → B) → ¬ (A → ¬ B) and (A → ¬ B) → ¬ (A → B). They are theorems…
Bivalence: The Principle of True or False
Bivalence asserts that every proposition is definitively either true or false, a cornerstone of classical logic. It excludes the possibility of a third truth value or indeterminate states, ensuring a…
Binary Relation: Understanding Relationships Between Sets
A binary relation defines a connection between elements of one or two sets. It's fundamental in mathematics, logic, and computer science for modeling connections like 'less than' or 'is a…
Binary Function
A binary function is a fundamental concept in mathematics and logic, taking exactly two inputs to produce a single output. It's commonly used for operations like addition, subtraction, and logical…
Bijective Functions: The Ultimate One-to-One Correspondence
A bijective function is a powerful mathematical concept, acting as a perfect bridge between two sets. It's both injective (one-to-one) and surjective (onto), ensuring every element has a unique partner…
Biconditional Statement in Logic
A biconditional statement in logic connects two propositions, asserting that they are true if and only if they have the same truth value. It's often symbolized as P ↔ Q.
Understanding Bias: Definition, Types, and Impact
Bias is a systematic deviation from neutrality, objectivity, or fairness. It arises from tendencies or inclinations, significantly impacting statistical analysis, cognitive processes, and decision-making across various fields.
Brouwer-Heyting-Kolmogorov Interpretation
The Brouwer-Heyting-Kolmogorov (BHK) interpretation equates statement truth with proof existence, forming the core of constructivist logic. It emphasizes constructive evidence over classical negation.
Provability Predicate
A provability predicate is a mathematical function that determines whether a statement is provable within a given formal system. It's fundamental in computability theory and logic, linking syntax and semantics.
Begging the Question: Understanding Circular Reasoning
Begging the question is a logical fallacy where an argument's conclusion is already assumed in its premise, creating a circular reasoning loop that fails to prove anything new.