For questions about three-valued logic and other non-classical logics. Please use the more specific tags 'modal-logic' and 'fuzzy-logic' instead of this tag if they apply.
Questions tagged [nonclassical-logic]
131 questions
106
votes
23 answers
Is math built on assumptions?
I just came across this statement when I was lecturing a student on math and strictly speaking I used:
Assuming that the value of $x$ equals , ...
One of my students just rose and asked me:
Why do we assume so much in math? Is math…
Anz Joy
- 1,448
31
votes
12 answers
Tricks for Constructing Hilbert-Style Proofs
Several times in my studies, I've come across Hilbert-style proof systems for various systems of logic, and when an author says, "Theorem: $\varphi$ is provable in system $\cal H$," or "Theorem: the following axiomatizations of $\cal H$ are…
Alex Kocurek
- 3,081
26
votes
0 answers
Was von Neumann's 1954 ICM address "Unsolved Problems in Mathematics" outdated?
I recently tried to "explain" the generalized probability theory aspect of quantum theory (as one common part of both quantum field theory and quantum mechanics), in the sense of motivations for the different parts of Qiaochu Yuan's post on…
Thomas Klimpel
- 7,608
20
votes
2 answers
Semantics for minimal logic
Minimal logic is a fragment of intuitionistic logic that rejects not only the classical law of excluded middle (as intuitionistic logic does), but also the principle of explosion (ex falso quodlibet). Essentially, from proof-theoretical viewpoint,…
Taroccoesbrocco
- 18,243
13
votes
14 answers
A proportionality puzzle: If half of $5$ is $3$, then what's one-third of $10$?
My professor gave us this problem.
In a foreign country, half of 5 is 3. Based on that same proportion, what's one-third of 10?
I removed my try because it's wrong.
user140581
- 147
13
votes
5 answers
Why do we prefer classical logic over non-classical logic?
In classical logic, we have paradoxes like paradoxes of material implication. If non-classical logic like relevance logic fixes those problems, why do we still continue to use classical logic?
Zeus
- 855
- 9
- 16
10
votes
1 answer
Defined negation in intuitionistic linear logic
Is it possible to define a negation in intuitionistic linear logic, the way one does in intuitionistic logic, i.e. $A^{\bot} \equiv A \multimap \mathbf{0}$ (or, as it would be written in intuitionistic logic, $\neg A \equiv A \to \bot$)?
While I can…
wen
- 203
9
votes
1 answer
Is there an intermediate logic between Minimal Logic and Intuitionistic Logic?
The existence of intermediate logics between intuitionistic logic and classical logic is well known (for example, adding $(A \to B) \lor (B \to A)$ as an "axiom of linearity" to Heyting's logic defines Gödel-Dummett logic, a logic stronger than…
8
votes
4 answers
Good book for learning and practising axiomatic logic
I want to learn axiomatic (Hilbert style ) logic.
not just a book that says that it exist and is an good way to proof theorems.
What is a good book to learn and practice this method?
would like:
- a book published after 2000
- not limited to a…
Willemien
- 6,730
7
votes
4 answers
Multiple Conditioning on Event Probabilities
I am trying to understand what's wrong with the following logic related to "multiple conditioning." Why is the probability of [(A given B) given C] not the same as the probability of [A given (B and C)] ? I know it's not true, but only because…
Bill
- 71
7
votes
6 answers
Book about different kinds of logic.
I'm searching for a book that talks about different kinds of logic (esoteric and particular ones too) and their uses and differences.
Does such a book exist?
lds
- 105
7
votes
3 answers
Neither true nor false? Paradoxes about ill-formed statements
In the appendix of Terence Tao's book Analysis, he writes:
Thus well-formed statements can be either true or false; ill-formed
statements are considered to be neither true nor false.
A more subtle example of an ill-formed statement is $ \ 0/0 =…
Sky subO
- 407
7
votes
3 answers
Looking for a simple proof of the independence of the law of excluded middle
I have seen a number of excellent posts on the difference between intuitionist propositional logic (IPL) and classical propositional logic (CPL), all of which state that IPL is agnostic on the law of excluded middle (LEM) or its equivalent forms. I…
Nat Kuhn
- 307
7
votes
2 answers
Quicksort with Trivalued Logic
Does anyone know a way to do a quick sort with trivalued logic?
The problem I’m trying to solve is this: I’m trying to display a view of a complex 3d object from a given viewing angle. I’ve broken the object into many 2d surfaces that I can draw…
6
votes
4 answers
What obstacles prevent three-valued logic from being used as a modal logic?
I am familiar with many of the surveys of many valued logic referenced in the SEP article on many valued logic, such as Ackermann, Rescher, Rosser and Turquette, Bolc and Borowic, and Malinowski. It is asserted in the article that "Many-valued logic…
Confutus
- 842