five properties that a theory may possess. These include the disjunction property (DP), the existence property (EP), and three additional properties: The...

realizability can be applied to prove the disjunction and existence properties for intuitionistic theories and to extract programs from proofs, as in proof...

this is that its restrictions produce proofs that have the disjunction and existence properties, making it also suitable for other forms of mathematical...

and yields a system where disjunction behaves more like in classical logic than intuitionistic logic, i.e. the disjunction and existence properties don't...

categorical algebra. For instance, Freyd gave a proof of the disjunction and existence properties of intuitionistic logic this way. These three themes are...

and complete with respect to intuitionistic logic and admits a similar cut-elimination proof. This can be used in proving disjunction and existence properties...

conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: The negation of "A and B" is the same...

exchange, constructive set theories can exhibit attractive disjunction and existence properties, as is familiar from the study of constructive arithmetic...

thesis, more such metalogical existence statements have been obtained. Computable function Disjunction and existence properties Realizability Troelstra, A...

algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra...

meta-logical properties. For example, if a theory T {\displaystyle {\mathsf {T}}} exhibits the disjunction property, then if it proves a disjunction T ⊢ ϕ ∨...

an infinite disjunction and is therefore inadmissible: first order logic permits quantifiers over one type and cannot capture properties or subsets of...

proposition p and proposition q then e is also a truthmaker for p. The disjunction principle states that if entity e is a truthmaker for the disjunction of proposition...

disjunction introduction but keep disjunctive syllogism and transitivity. In this approach, rules of natural deduction hold, except for disjunction introduction...

corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean...

{\mathrm {n} }})} So these properties are metalogical equivalent in Heyting arithmetic. The existence and disjunction property in fact still holds when...

Retrieved 2009-05-14. Gygax: "Anagrams of my name are exclusively my property according to my settlement agreement with TSR, so that is how I can use...

corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨, which would constitute a semiring)...

propositions, and the only other allowed connectives are conjunction and disjunction. negative proposition A proposition that asserts the non-existence or absence...

deriving an explosion, typically including disjunctive syllogism, disjunction introduction, and reductio ad absurdum. The metamathematical value of the principle...

universal quantifier, the existential quantifier distributes over logical disjunctions: ∃ x ∈ X P ( x ) ∨ Q ( x ) →   ( ∃ x ∈ X P ( x ) ∨ ∃ x ∈ X Q ( x ) )...

from Kant's tables, and under the heading of Relation, Kant lists inter alia the three relationship types of Disjunction, Causality and Inherence. The three...

concerns the empty conjunction and the empty disjunction. The semantic clauses for, respectively, conjunctions and disjunctions are given by A ⊨ ϕ 1 ∧ ⋯ ∧...

Liar as both true and false. In this way, the law of excluded middle is true, but because truth itself, and therefore disjunction, is not exclusive,...

understands realism about physical objects to entail the existence of the properties of momentum and position for quanta. Since the uncertainty principle...

advantages include the conjunction fallacy, the disjunction fallacy, the failures of the sure-thing principle, and question-order bias in judgement.: 752  If...

some particular number. Further, a constructive framework with the disjunction property then cannot prove P ∨ ¬ P {\displaystyle P\lor \neg P} either. There...

alternate experience of existence that forms life in a different manner. A common effect on an individual of this disjunction between subjectivities is...

logic for second-order set theory, permitting infinitary conjunctions and disjunctions of length < κ {\displaystyle <\kappa } . κ {\displaystyle \kappa }...

immersions and try to eliminate multiple points, seeing if one can do this without introducing other singularities – studying "multiple disjunctions". This...