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Assumption-Based Argumentation with Preferences
Assumption-Based Argumentation with Preferences

Revising the AGM Postulates
Revising the AGM Postulates

Principia Logico-Metaphysica (Draft/Excerpt)
Principia Logico-Metaphysica (Draft/Excerpt)

Announcement as effort on topological spaces
Announcement as effort on topological spaces

How to Go Nonmonotonic Contents  David Makinson
How to Go Nonmonotonic Contents David Makinson

Per Lindström FIRST
Per Lindström FIRST

Category Theory Lecture Notes for ESSLLI Michael Barr Department
Category Theory Lecture Notes for ESSLLI Michael Barr Department

... if the source of g is the target of f . This means that composition is a function whose domain is an equationally defined subset of G1 × G1 : the equation requires that the source of g equal the target of f . It follows from this and C–1 that in C–2, one side of the equation is defined if and only i ...
Incompleteness
Incompleteness

venn diagram review
venn diagram review

Hilbert`s Program Then and Now
Hilbert`s Program Then and Now

Chapter 13 BOOLEAN ALGEBRA
Chapter 13 BOOLEAN ALGEBRA

... Notice that the two definitions above refer to "...a greatest lower bound" and "a least upper bound." Any time you define an object like these you need to have an open mind as to whether more than one such object can exist. In fact, we now can prove that there can't be two greatest lower bounds or t ...
Some Aspects and Examples of Innity Notions T ZF
Some Aspects and Examples of In nity Notions T ZF

Logic and Proof
Logic and Proof

Untitled
Untitled

... Though the bulk of the text has remained unchanged from the first edition, there are a number of changes, large and small, that will hopefully improve the text. As always, any remaining problems are solely the fault of the author. ...
The Premiss-Based Approach to Logical Aggregation Franz Dietrich & Philippe Mongin
The Premiss-Based Approach to Logical Aggregation Franz Dietrich & Philippe Mongin

Inductive Types in Constructive Languages
Inductive Types in Constructive Languages

Hilbert`s Program Then and Now - Philsci
Hilbert`s Program Then and Now - Philsci

Problems on Discrete Mathematics1 (Part I)
Problems on Discrete Mathematics1 (Part I)

... correct. But, in general, we are not able to do so because the domain is usually an infinite set, and even worse, the domain can be uncountable, e.g., real numbers. To overcome this problem, we divide the domain into several categories and make sure that those categories cover the domain. Then we ex ...
Forking in simple theories and CM-triviality Daniel Palacín Cruz
Forking in simple theories and CM-triviality Daniel Palacín Cruz

PhD Thesis First-Order Logic Investigation of Relativity Theory with
PhD Thesis First-Order Logic Investigation of Relativity Theory with

... devoted to dynamics. We represent motion as the changing of spatial location in time. Thus we use reference frames for coordinatizing events (sets of bodies). Quantities are used for marking time and space. The structure of quantities is assumed to be an ordered field in place of the field of real n ...
Nominal Monoids
Nominal Monoids

Proofs in theories
Proofs in theories

abdullah_thesis_slides.pdf
abdullah_thesis_slides.pdf

... threshold t such that the values (#Type1 ,...,#Typen ) are counted only upto a threshold t and anything ≥ t is considered ∞. Two structures A and B, are said to be d-equivalent with threshold t if their type signatures with radius d are equal. It is denoted A ∼d,t B. Theorem Given d ∈ N and two stru ...
lecture notes in logic - UCLA Department of Mathematics
lecture notes in logic - UCLA Department of Mathematics

... Together with (2), this means that for all x, y in K, x · y = 0 ⇐⇒ x = 0 or y = 0. (4) For all x, y, z, x · (y + z) = x · y + x · z (the distributive law ). Basic examples of fields are the rational numbers Q, the real numbers R and the complex numbers C, with universes Q, R, C respectively and the ...
Bridge to Abstract Mathematics: Mathematical Proof and
Bridge to Abstract Mathematics: Mathematical Proof and

1 2 3 4 5 ... 37 >

Naive set theory

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using a formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday usage of set theory concepts in contemporary mathematics.Sets are of great importance in mathematics; in fact, in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory can be seen as a stepping-stone to more formal treatments, and suffices for many purposes.
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