proceedings version
... A here-and-there model (HT model) is made up of two sets of propositional variables H (‘here’) and T (‘there’) such that H ⊆ T . The logical language to talk about such models has connectives ⊥, ∧, ∨, and ⇒. The latter is interpreted in a non-classical way and is therefore different from the materia ...
... A here-and-there model (HT model) is made up of two sets of propositional variables H (‘here’) and T (‘there’) such that H ⊆ T . The logical language to talk about such models has connectives ⊥, ∧, ∨, and ⇒. The latter is interpreted in a non-classical way and is therefore different from the materia ...
natural numbers
... Cantor's diagonal argument: uncountability of reals The diagonal method, was published in 1891 by Georg Cantor as a proof that there are infinite sets which cannot be put into 1-1 correspondence with the infinite set of natural numbers. Such sets are now known as uncountable sets, and the size of i ...
... Cantor's diagonal argument: uncountability of reals The diagonal method, was published in 1891 by Georg Cantor as a proof that there are infinite sets which cannot be put into 1-1 correspondence with the infinite set of natural numbers. Such sets are now known as uncountable sets, and the size of i ...
An Overview of Intuitionistic and Linear Logic
... Constructivism is a point of view concerning the concepts and methods used in mathematical proofs, with preference towards constructive concepts and methods. It emerged in the late 19th century, as a response to the increasing use of abstracts concepts and methods in proofs in mathematics. Kronecker ...
... Constructivism is a point of view concerning the concepts and methods used in mathematical proofs, with preference towards constructive concepts and methods. It emerged in the late 19th century, as a response to the increasing use of abstracts concepts and methods in proofs in mathematics. Kronecker ...
Exercise
... P(x) it is not enough to show that P(a) is true for one or some a’s. 2. To show that a statement of the form x P(x) is FALSE, it is enough to show that P(a) is false for one a ...
... P(x) it is not enough to show that P(a) is true for one or some a’s. 2. To show that a statement of the form x P(x) is FALSE, it is enough to show that P(a) is false for one a ...
Justification logic with approximate conditional probabilities
... First-order variants of LPPS have recently been studied by Ikodinović et al. [18]. Marchioni and Godo [26] present a fuzzy logic with conditional probabilities that uses non-standard probabilities. There are two main contributions of this paper. The first, obviously, is the introduction of operator ...
... First-order variants of LPPS have recently been studied by Ikodinović et al. [18]. Marchioni and Godo [26] present a fuzzy logic with conditional probabilities that uses non-standard probabilities. There are two main contributions of this paper. The first, obviously, is the introduction of operator ...
DOC - John Woods
... determine the truth values of formal sentences. John Burgess is good on this point: “To avoid confusion, one could distinguish “formal semantics” or model theory from “linguistic semantics” or meaning theory; but it is best to avoid “semantics” altogether”. (Philosophical Logic, Princeton, 2009; p. ...
... determine the truth values of formal sentences. John Burgess is good on this point: “To avoid confusion, one could distinguish “formal semantics” or model theory from “linguistic semantics” or meaning theory; but it is best to avoid “semantics” altogether”. (Philosophical Logic, Princeton, 2009; p. ...
Logic and Categories As Tools For Building Theories
... 2. f is surjective iff f is epic. Proof We show 1. Suppose f : X → Y is injective, and that f ◦ g = f ◦ h, where g, h : Z → X. Then for all z ∈ Z: ...
... 2. f is surjective iff f is epic. Proof We show 1. Suppose f : X → Y is injective, and that f ◦ g = f ◦ h, where g, h : Z → X. Then for all z ∈ Z: ...
mplications of Cantorian Transfinite Set Theory
... David Hilbert described Cantor's work as:“...the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.” "I see it but I don't believe it.” Georg Cantor on his own theory. “…the infinite is nowhere to be found in reality” David Hilbert. ...
... David Hilbert described Cantor's work as:“...the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.” "I see it but I don't believe it.” Georg Cantor on his own theory. “…the infinite is nowhere to be found in reality” David Hilbert. ...
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
... successor’, ‘2 has a successor’, etc. for each natural number; as a consequence of we have the sentence ‘Every natural number has a successor’. On a rather abstract level of logic, one may envisage a deduction corresponding to the consequence relation in this example (the rule justifying this ded ...
... successor’, ‘2 has a successor’, etc. for each natural number; as a consequence of we have the sentence ‘Every natural number has a successor’. On a rather abstract level of logic, one may envisage a deduction corresponding to the consequence relation in this example (the rule justifying this ded ...
The modal logic of equilibrium models
... about the there-world: a valuation that is at least as strong as the actual valuation; and [S] allows to talk about all here-worlds that are possible if we take the actual world as a there-world: it quantifies over all valuations that are weaker than the actual world. This language is again interpr ...
... about the there-world: a valuation that is at least as strong as the actual valuation; and [S] allows to talk about all here-worlds that are possible if we take the actual world as a there-world: it quantifies over all valuations that are weaker than the actual world. This language is again interpr ...
