Synonymer & Oplysninger om | engelsk ord PROVABILITY

Eksempler på brug af PROVABILITY i en sætning

• Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
• The modal-logical treatment of provability helped demonstrate the "intensionality" of Gödel's Second Incompleteness Theorem, meaning that the theorem's correctness depends on the precise formulation of the provability predicate.
• In outline, the key to Willard's construction of his system is to formalise enough of the Gödel machinery to talk about provability internally without being able to formalise diagonalisation.
• These related representations provide a well defined mathematical apparatus for studying the relationship between truth modalities (possibly true vs necessarily true, studied in modal logic) and notions of provability and refutability (studied in intuitionistic logic) and is thus deeply connected to the theory of modal companions of intermediate logics.
• In "The polymodal logic of provability" Japaridze proved the arithmetical completeness of this system, as well as its inherent incompleteness with respect to Kripke frames.
• As in regular logic programming, programs are queried about the provability of a goal, which itself may contain constraints in addition to literals.
• The theory of evidential reasoning also defines non-additive probabilities of probability (or epistemic probabilities) as a general notion for both logical entailment (provability) and probability.
• His areas of research include logic (theories of truth and modality, paradox, conditionals, nonmonotonic reasoning, dynamic doxastic logic), epistemology (belief, inference, belief revision, foundations of probability, Bayesianism), philosophy of mathematics (structuralism, informal provability, abstraction, criteria of identity), philosophy of language (indeterminacy of translation, compositionality), cognitive science (symbolic representation and neural networks, metacognition), philosophy of science (empirical content, measurement theory), and history of philosophy (logical positivism, Carnap, Quine).
• Japaridze's polymodal logic (GLP) is a system of provability logic with infinitely many provability modalities.

Sideforberedelse tog: 2.244,22 ms.