Structural Proof Theory
... of proof. Sequent calculus, instead, has been developed in various directions. One line leads from Gentzen through Ketonen, Kleene, Dragalin, and Troelstra to what are known as contraction-free systems of sequent calculus. Each of these logicians added some essential discovery, until a gem emerged. ...
... of proof. Sequent calculus, instead, has been developed in various directions. One line leads from Gentzen through Ketonen, Kleene, Dragalin, and Troelstra to what are known as contraction-free systems of sequent calculus. Each of these logicians added some essential discovery, until a gem emerged. ...
venn diagram review
... all the elements in the universal set that are not identical a set of elements that work well with a given set all the elements of a universal set that do not belong to a subset of it all the elements that are the opposite of the elements in a given set ...
... all the elements in the universal set that are not identical a set of elements that work well with a given set all the elements of a universal set that do not belong to a subset of it all the elements that are the opposite of the elements in a given set ...
Principia Logico-Metaphysica (Draft/Excerpt)
... Part I: Prophilosophy Part II: Philosophy Part III: Metaphilosophy Part IV: Technical Appendices, Bibliography, Index This excerpt was generated on October 28, 2016 and contains: • Part II: Chapter 7: The Language ...
... Part I: Prophilosophy Part II: Philosophy Part III: Metaphilosophy Part IV: Technical Appendices, Bibliography, Index This excerpt was generated on October 28, 2016 and contains: • Part II: Chapter 7: The Language ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
some results on locally finitely presentable categories
... limits and filtered colimits. In §1, we give an essentially self-contained account of the 'duality' of small categories with finite limits and l.f.p. categories. This duality amounts to an equivalence of the 2-categories Lexop and LFP, the 2-category of l.f.p. categories, with morphisms the functors ...
... limits and filtered colimits. In §1, we give an essentially self-contained account of the 'duality' of small categories with finite limits and l.f.p. categories. This duality amounts to an equivalence of the 2-categories Lexop and LFP, the 2-category of l.f.p. categories, with morphisms the functors ...
A survey on Interactive Theorem Proving
... that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insight, the activity of checking a given mahematical argument is an objective activity; mathematical correctness should not be decided by a socia ...
... that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insight, the activity of checking a given mahematical argument is an objective activity; mathematical correctness should not be decided by a socia ...
PhD Thesis First-Order Logic Investigation of Relativity Theory with
... answer the why-type questions of relativity. For example, we can take the twin paradox theorem and check which axiom of special relativity was and which one was not needed to derive it. The weaker an axiom system is, the better answer it offers to the question: “Why is the twin paradox true?”. The t ...
... answer the why-type questions of relativity. For example, we can take the twin paradox theorem and check which axiom of special relativity was and which one was not needed to derive it. The weaker an axiom system is, the better answer it offers to the question: “Why is the twin paradox true?”. The t ...
Logic in Nonmonotonic Reasoning
... one lock produces an indirect effect of opening the suitcase if and only if the other lock is open. Such derived effects should be taken into account when combined with the inertia assumption, since they override the latter. The ramification problem has raised general questions on the nature of caus ...
... one lock produces an indirect effect of opening the suitcase if and only if the other lock is open. Such derived effects should be taken into account when combined with the inertia assumption, since they override the latter. The ramification problem has raised general questions on the nature of caus ...
Modal Logic - Web Services Overview
... Algebraic models for modal logic are still a research issue In fuzzy of MV logic operation on uncertainties creates other uncertainties, better or worse but never certainties 7. In modal logic you can derive certainties from uncertainties ...
... Algebraic models for modal logic are still a research issue In fuzzy of MV logic operation on uncertainties creates other uncertainties, better or worse but never certainties 7. In modal logic you can derive certainties from uncertainties ...
A pragmatic dialogic interpretation of bi
... identify, among the mathematical models of bi-intuitionism, those which may be regarded as its intended interpretations. The quest for an intended interpretation of a formal system often arises when several mathematical structures have been proposed to characterise an informal, perhaps vague notion ...
... identify, among the mathematical models of bi-intuitionism, those which may be regarded as its intended interpretations. The quest for an intended interpretation of a formal system often arises when several mathematical structures have been proposed to characterise an informal, perhaps vague notion ...
Set theory
Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.