Hilbert`s Program Then and Now
... between the basic concepts and the axioms. Of basic importance for an axiomatic treatment are, so Hilbert, investigation of the independence and, above all, of the consistency of the axioms. In his 1902 lectures on the foundations of geometry, he puts it thus: Every science takes its starting point ...
... between the basic concepts and the axioms. Of basic importance for an axiomatic treatment are, so Hilbert, investigation of the independence and, above all, of the consistency of the axioms. In his 1902 lectures on the foundations of geometry, he puts it thus: Every science takes its starting point ...
Introduction to Linear Logic
... The proof-rules for Intuitionistic Logic can then be considered as methods for defining functions such that a proof of a sequent Γ ` B gives rise to a function which assigns a proof of the formula B to a list of proofs proving the respective formulae in the context Γ. Note that tertium non datur, A ...
... The proof-rules for Intuitionistic Logic can then be considered as methods for defining functions such that a proof of a sequent Γ ` B gives rise to a function which assigns a proof of the formula B to a list of proofs proving the respective formulae in the context Γ. Note that tertium non datur, A ...
Fichte`s Legacy in Logic
... Wissenschaftslehre should itself lead us to recognize a new logical form of judgment: the thetic judgment. Cataloging the various forms of judgment has long been a central part of logical theory. Just as the syllogistic figures specify the allowable forms of inference (the forms in accordance with w ...
... Wissenschaftslehre should itself lead us to recognize a new logical form of judgment: the thetic judgment. Cataloging the various forms of judgment has long been a central part of logical theory. Just as the syllogistic figures specify the allowable forms of inference (the forms in accordance with w ...
Hilbert`s Program Then and Now - Philsci
... In about 1920, Hilbert came to reject Russell’s logicist solution to the consistency problem for arithmetic, mainly for the reason that the axiom of reducibility cannot be accepted as a purely logical axiom. In lectures from the Summer term 1920, he concluded that “the aim of reducing set theory, an ...
... In about 1920, Hilbert came to reject Russell’s logicist solution to the consistency problem for arithmetic, mainly for the reason that the axiom of reducibility cannot be accepted as a purely logical axiom. In lectures from the Summer term 1920, he concluded that “the aim of reducing set theory, an ...
The Foundations
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
The Foundations
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
Theories and uses of context in knowledge representation and
... believe that a completely general representation of knowledge is impossible in practice, and – more interestingly – perhaps not even desirable. Indeed, whatever language and facts we choose to represent, there is always a situation in which the stated facts or the language itself are not adequate. H ...
... believe that a completely general representation of knowledge is impossible in practice, and – more interestingly – perhaps not even desirable. Indeed, whatever language and facts we choose to represent, there is always a situation in which the stated facts or the language itself are not adequate. H ...
Formal deduction in propositional logic
... ’Contrariwise,’ continued Tweedledee, ’if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.’ (Lewis Caroll, “Alice in Wonderland”) Formal deduction in propositional logic ...
... ’Contrariwise,’ continued Tweedledee, ’if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.’ (Lewis Caroll, “Alice in Wonderland”) Formal deduction in propositional logic ...
