Understanding Predicates and Their Representation of Functions and Sets
A predicate P represents a function f if P(x1,...,xn,y) is true iff f(x1,...,xn)=y. A unary predicate P represents set S if P(x) is true iff x is in S. This…
Relevance Logic
Relevance logic is a non-classical logic designed to ensure premises are relevant to the conclusion, overcoming paradoxes found in material implication. It focuses on logical connection.
Relative Consistency Proof
A relative consistency proof demonstrates that if a system S is consistent, adding new axioms to S also maintains consistency. This is crucial for comparing the foundational strength of different…
Relational Semantics
Relational semantics interprets logical languages using relations between possible worlds or states of affairs. It's a key tool for understanding modal and temporal logics, defining truth based on these inter-world…
Register Machine: A Computational Model
A register machine is a theoretical computing model using registers and instructions to perform calculations. It's an alternative to the Turing machine, offering a different perspective on computation.
Register Computable
A computation is register computable if it can be performed by a register machine. This concept is fundamental in theoretical computer science, defining a class of problems solvable by a…
Refutation: Disproving Falsehoods
Refutation is the critical process of disproving or demonstrating the falseness of a statement, argument, or theory. It involves presenting evidence and logical reasoning to invalidate claims and establish the…
Reflexivity in Relations
Reflexivity means every element in a set is related to itself. This fundamental property is crucial in understanding various mathematical and computational structures, like equality.
Referential Opacity Explained
Referential opacity describes expressions where replacing a co-referential term might alter the truth value. This phenomenon is common in intensional contexts, such as belief statements.
Understanding Reference in Semantics
Reference is the fundamental relationship between linguistic expressions and the real world. It's how words and symbols connect to objects, concepts, and events, forming the basis of meaning and communication.