# Tagged Questions

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.

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### Are there any examples of consistent proper axiomatic extensions of classical logic?

By a proper axiomatic extension, I mean a logic with the same set of well formed formulas as classical logic, but with the set of theorems of the logic a proper superset of the theorems of classical ...
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### Interpretation of relations in varying-domain models of F.O. modal logic

I am studying the book "First Order Modal Logic" By Fitting and Mendelsohn. In their definition of interpretation for varying domain models (def 4.7.3 pg 103), the interpretation of a relation in a ...
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### Logical equivalence implication between Kleene and Classical logic

For any propositional assertions, $\phi$ and $\psi$, expressed using only the standard propositional logical connectives $\{\lnot,\land,\lor,\rightarrow,\iff\}$, if $\phi$ and $\psi$ are logically ...
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### “Relative unsatisfiability” of SAT instances

There's a natural way to view any SAT instance as a variety: just replace the Boolean algebra $2$ of truth values with the corresponding Boolean ring $\mathbb{Z}/2\mathbb{Z}$. (See my answer to Is ...
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### Is ¬¬(¬¬P → P) provable in intuitionistic logic?

I have a feeling it's not, because ¬¬P → P is not provable. If it is, I'm not sure what kind of reductio I'd need to negate ¬(¬¬P → P). I believe a textbook somewhere said it was provable in ...
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### How to proofs work in three-valued Kleene logic?

In three-valued logics such as Kleene logic, there is a third truth value U, which represents "undefined", or "who knows?". It behaves like "either true or false", ...
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### Does the Law of the Excluded Middle imply syntactical completeness?

The Law of the Excluded Middle (LEM) states that for any proposition $p$, we have $\vdash p \lor \lnot p$. Syntactic completeness (a.k.a negation completeness) states that for any proposition $p$, ...
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### Logic & Reality [closed]

Maybe just a quick preface first before the question. I recently started a YouTube channel where I'm trying to clear up confusions I see on various (usually philosophical topics). In my 2nd video, the ...
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### 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 ...
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### Intuitionistic Logic and Classical Logic on the proof of (A or B)

In intuitionist logic, a proof of (A or B) means a proof of A, or a proof of B, whereas in Classical logic, a proof of (A or B) may be done withouth either proving A or proving B. I'm trying to ...
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### Is there a logic to formalize the concept of “understanding” [closed]

The question may seem little bit weird given that philosophers have been struggling to have a full grasp on the concept of "understanding". But I'm wondering if there are any logics (modal-based or ...
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### What are the different approachs to logic?

I have studied a little of logic (namely, FOL and propositional logic) using so-called "Hilbert style". I've heared that there are different approachs to logics like , deductions, trees, natural ...
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### A proportionality puzzle

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.
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### 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 ...
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### Reference request: preparation for learning a little smooth infinitesimal analysis?

I'm interested in learning a little smooth infinitesimal analysis. There is a free book by Kock: Smooth Differential Geometry, http://home.imf.au.dk/kock/ . As I dive into it, I feel that I'm not ...
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### 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)...
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### 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 ...