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Satisfiability -- Scholastic logic -- Second-order predicate -- Self-reference -- Sequent -- Sequent calculus -- Sequential logic -- Singular term -- Soundness -- Square of opposition -- Strict conditional -- Strict implication -- Strict logic -- Structural rule -- Sufficient condition -- Syllogism -- Syllogistic fallacy
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Scholastic and term
The term dates from medieval Scholastic philosophy, but was resurrected by Franz Brentano and adopted by Edmund Husserl.
The newspaper is published twice per term and was awarded the Columbia Scholastic Press Association's Silver Crown Award for high school newspapers in 1988.
Scholastic and Square
* 2004 The Cats in Krasinski Square, Illustrated by Wendy Watson ( Google Books edition, Scholastic Press, ISBN 978-0-439-43540-6 )
logic and Second-order
Second-order logic, for example, does not have a completeness theorem for its standard semantics ( but does have the completeness property for Henkin semantics ), and the same is true of all higher-order logics.
Second-order logic is in turn extended by higher-order logic and type theory.
Second-order logic also includes variables quantifying over functions, and other variables as explained in the section Syntax below.
Second-order logic is more expressive than first-order logic.
Second-order logic with Henkin semantics is not more expressive than first-order logic.
* Second-order logic
* Second-order logic
* Second-order logic corresponds to PH.
* Second-order logic with a transitive closure ( commutative or not ) yields PSPACE, the problems solvable in polynomial space.
* Second-order logic with a least fixed point operator gives EXPTIME, the problems solvable in exponential time.
# REDIRECT Second-order logic
# redirect Second-order logic
# redirect Second-order logic
logic and predicate
Frege's Begriffsschrift ( 1879 ) introduced both a complete propositional calculus and what is essentially modern predicate logic.
* Extension ( predicate logic )
* Extension ( predicate logic ), the set of tuples of values that satisfy the predicate
The process of abstract axiomatization as exemplified by Hilbert's axioms reduces geometry to theorem proving or predicate logic.
This is the case of the Mycin and Dendral expert systems, and of, for example, fuzzy logic, predicate logic ( Prolog ), symbolic logic and mathematical logic.
It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic ( a less precise term ).
The adjective " first-order " distinguishes first-order logic from higher-order logic in which there are predicates having predicates or functions as arguments, or in which one or both of predicate quantifiers or function quantifiers are permitted.
In first-order logic, however, the sentences can be expressed in a more parallel manner using the predicate Phil ( a ), which asserts that the object represented by a is a philosopher.
The language ’ s grammar is based on predicate logic, which is why it was named Loglan, an abbreviation for " logical language ".
It also became clear that such clauses could be restricted to definite clauses or Horn clauses, where < tt > H </ tt >, < tt > B < sub > 1 </ sub ></ tt >, …, < tt > B < sub > n </ sub ></ tt > are all atomic predicate logic formulae, and that SL-resolution could be restricted ( and generalised ) to LUSH or SLD-resolution.
The analogue of conjunction for a ( possibly infinite ) family of statements is universal quantification, which is part of predicate logic.
Logical connectives along with quantifiers are the two main types of logical constants used in formal systems such as propositional logic and predicate logic.
Just as propositional logic can be seen as an advancement from the earlier syllogistic logic, Gottlob Frege's predicate logic was an advancement from the earlier propositional logic.
Also in first-order predicate logic:
logic and Self-reference
* Craig Smoryński, Self-reference and modal logic.
logic and calculus
Categorical logic is now a well-defined field based on type theory for intuitionistic logics, with applications in functional programming and domain theory, where a cartesian closed category is taken as a non-syntactic description of a lambda calculus.
An equivalent theoretical formulation, combinatory logic, is commonly perceived as more abstract than lambda calculus and preceded it in invention.
Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the foundations of mathematics.
He had made advances in the areas of analysis, foundations and logic, made many contributions to the teaching of calculus and also contributed to the fields of differential equations and vector analysis.
Robinson's approach, called non-standard analysis, uses technical machinery from mathematical logic to create a theory of hyperreal numbers that interpret infinitesimals in a manner that allows a Leibniz-like development of the usual rules of calculus.
In logic, a many-or multi-valued logic is a propositional calculus in which there are more than two values.
* In mathematical logic and computer science, lambda is used to introduce an anonymous function expressed with the concepts of lambda calculus.
* The language Unlambda is a functional programming language based upon combinatory logic, a simplification of the lambda calculus that does not involve the lambda at all, hence the un-prefix.
The use of mathematical logic to represent and execute computer programs is also a feature of the lambda calculus, developed by Alonzo Church in the 1930s.
In mathematical logic, a propositional calculus or logic ( also called sentential calculus or sentential logic ) is a formal system in which formulas of a formal language may be interpreted as representing propositions.
Although propositional logic ( which is interchangeable with propositional calculus ) had been hinted by earlier philosophers, it was developed into a formal logic by Chrysippus and expanded by the Stoics.
Gottfried Leibniz has been credited with being the founder of symbolic logic for his work with the calculus ratiocinator.
Lambda calculus ( also written as λ-calculus or called " the lambda calculus ") is a formal system in mathematical logic for expressing computation by way of variable binding and substitution.
A major example of this is the Curry – Howard correspondence, which gives a correspondence between different systems of typed lambda calculus and systems of formal logic.
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