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...

categorical algebra. For instance, Freyd gave a proof of the disjunction and existence properties of intuitionistic logic this way. History of topos theory...

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

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

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...

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

some of its extensions exhibit the disjunction property instead, implying one of the disjuncts of any disjunction individually would have to be derivable...

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

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

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

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...

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

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

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

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...

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

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

for the existence of an actually infinite being. First from the view of the Relative Properties of God and second from the Absolute Properties of God....

non-disjunctive properties and relations to non-disjunctive subjects. Some eliminativists reject intentionality while accepting the existence of qualia. Other...

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

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...

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

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

by ruling out the existence of counter-examples, the induction principle thus plays a similar role as the excluded middle disjunction, but the former is...

conjunctions or disjunctions with less than κ constituents is known as Lκω. For example, Lω1ω permits countable conjunctions and disjunctions. The set of...

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

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

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,...