# Questions tagged [nonclassical-logic]

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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### Proof within Łukasiewicz's infinite-valued logic $Ł_{א}$

Using the axiom system for Łukasiewicz's infinite-valued logic $Ł_{א}$, I need to construct a proof of the following: ⊢ (A → B) ∨ (B → A) ⊢ (A → (B → C)) → (B → (A → C)) A → B ⊢ (A ∧ C) → B A → B ⊢ ¬B ...
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### Books on co-Heyting algebras (with a view to their logics).

I would like to know more about co-Heyting algebras, particularly from the perspective of their logics (like paraconsistent logics). What books are available out there on the topic? It might be that ...
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### Does Bi-Intuitionistic Logic turn Classical in sufficiently strong first-order theories?

Bi-Intuitionistic Logic adds to Intuitionistic Logic a binary connective $←$ known as co-implication or subtraction. A weak negation $\sim A$ is defined for Bi-Intuitionistic Logic as $\top ← A$; Bi-...
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### Is there a way to define classical implication in this logic?

I’m asking this question so that I may provide my own answer to it and share what I’ve discovered. I’ve already posted about a logic that results from modifying the Gödel-McKinsey-Tarski translation ...
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### Does this outwit Rosser's trick? [closed]

Reading about Rosser's trick made me instantly curious about the following question: Can we devise a logic (which semantically encapsulates useful maths - define that as you will) in which for any ...
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### Examples of finitely-valued logics that aren't algebraizable

I was reading this question which asks about the equivalent of Boolean algebras for relevant logic. In the comments, Noah Schweber mentions that the relevant logic E is not algebraizable. In the book ...
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### Boolean algebra is to classical logic like what is to relevant logic?

The Question: Boolean algebra is to classical logic like what is to relevant logic? Context: I guess this is a terminology question, so there's not much I can add, except that I've been interested ...
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### What exactly are capture and release?

Motivation: I'm interested in how different people resolve the Liar paradox and other, related phenomena, like the revenge Liar paradoxes, and so on. I have a copy of "Formal Theories of Truth,&...
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### Has this logic already been studied?

I have been spending the better part of a year thinking about the subtleties involved in balancing natural language intuitions for logic with the power and efficacy that Classical Logic and ...
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### Examples of propositional logics with conditionals based on conditional probability?

Are there any propositional logics with conditionals whose semantics are based on conditional probability? I can see two design challenges that come with defining a conditional-probability-flavored ...
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### Is there a list of logics?

There are a lots of logics. Some of them are: Propositional logic Predicate logic Second order logic $n$ order logic Fuzzy logic Modal logic Multivalued logic etc So I`d like to know whether there ...
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### What are the automorphisms on the strucuture consisting of the nonzero vectors of a Hilbert space with the orthogonality relation?

Let $V$ be an infinite-dimensional complex Hilbert space. With this space we can associate a relational structure $V^+ = (V^+, \bot)$, where $V^+$ is the set of non-zero vectors in $V$, and $\bot$ ...
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### " Logic does not allow you to say this": is this assertion outdated?

I think one cannot say nowadays without further qualification " geometry does not allow you to say that the sum of a triangle's angles is less than 180 degrees". The sentence concerning the sum of ...
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### Relative strength and propositional indistinguishability of non-distributive lattices

Consider the class of bounded non-distributive lattices $\mathbf{Mn}$ ($n\geqslant 3$). From left to right: M3, M4, Mn Now consider a propositional language over $\{\wedge,\vee,\neg\}$ with the ...
I've just started looking into epistemic logic and belief revision approaches, and I'm struggling already with proving some basic properties. I am given the following definition: Let $\mathcal{L}_0$...