Classical Reductio Ad Absurdum
A robust form of reductio ad absurdum, it proves a proposition P by demonstrating that its negation ¬P leads to a contradiction, thus validating P.
Classical Logic
Classical logic, founded on bivalence, non-contradiction, and excluded middle, is the traditional system for propositional and predicate logic. It forms the bedrock of much formal reasoning.
The Classical Dilemma: A Rhetorical Tool of Inevitability
A classical dilemma presents two undesirable choices, both leading to the same inescapable conclusion. This rhetorical device, prevalent in logic and argumentation, highlights the inevitability of a specific outcome through…
Church–Turing Thesis
The Church-Turing thesis posits that any function computable by a human can be computed by a Turing machine. It defines the fundamental limits of what is computable, establishing a bedrock…
Church’s Theorem
Church's theorem proves the undecidability of fundamental decision problems in logic, like the Entscheidungsproblem. It demonstrates that no logic can be simultaneously consistent, complete, and effectively calculable.
Chronological Logic
Chronological logic, also known as temporal modal logic, deals with reasoning about time and events. It extends classical logic by incorporating operators that express temporal relationships, such as 'always,' 'sometime,'…
Causal Modal Logic
Causal modal logic extends standard modal logic with modalities for necessity, possibility, and causal relations. It enables formal analysis of causal statements and their implications.
Causal Logic
Causal logic explores the intricate relationships between causes and effects. It provides frameworks for representing and reasoning about how events influence one another, forming a crucial part of artificial intelligence…
Category Theory
Category theory is a branch of mathematics that abstracts algebraic structures and their relationships. It offers a unifying framework across diverse mathematical fields, focusing on structure and transformation.
Category Theory: A Foundation for Mathematical Structures
A category is a fundamental structure in mathematics and logic, comprising objects and the relationships (morphisms) between them. It provides a powerful abstract framework for studying diverse mathematical concepts and…