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Everything about Logical equality
Logical operator in propositional calculus
Logical equality is a logical operator that compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments have the same truth value, and False if they are different. In the case where formulas have free variables, we say two formulas are equal when their truth values are equal for all possible resolutions of free variables. It corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Logical equalityA 5-minute orientation
- Pick up a classic book: Collected WorksThe most-reprinted book on the subject
- Read the landmark paper: Comment on "Empty Ideas": Logical Positivist Analyses of Equality and RulesCited 5 times
- Go sideways: Truth tableA closely related topic
- Go sideways: Logical connectiveA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Comment on "Empty Ideas": Logical Positivist Analyses of Equality and Rules
Dependently-Typed Programming with Logical Equality Reflection
The undecidability of proof search when equality is a logical connective
Mathematical Postulates for the Logical Operations of Assertion, Conjunction, Negation and Equality
The [Im]Practicality of Religion and the Gender [In]Equality: A logical Analysis
Equality of consequence relations in finite-valued logical matrices
📚 Books worth reading
Collected WorksJohn Stuart Mill · 1869
Advances in Experimental Social PsychologyJames M. Olson · 2017
Essays on politics and societyJohn Stuart Mill · 1963- 📕Mythes égalitaires et pauvretésRaymonde Sechet-Poisson · 1989
- 📕al-Ḥijāj, mafhūmuhu wa-majālātuhḤāfīẓ Ismāʻīlī ʻAlawī · 2013
The philosophy of mathematicsW. S. Anglin · 1997
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which…
- Logical connective In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is an operator that combines or modifies…
- Logical biconditional In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication…
- Logical NOR In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical…
- Truth function In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and…
- Functional completeness In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining…
- Logical disjunction In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated…
- Exclusive or Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the…