# 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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### Czelakowski matrix semantics vs ordinary matrix semantics vs Co-Czelakowski matrix semantics

The kind of matrix semantics that I'm accustomed to seeing is something like $\langle A, F \rangle$ where $A$ is an algebra in some signature and $F$ is a subset of the carrier of $A$. A Czelakowski ...
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### Proof of the Local Deduction Theorem, for one of many logics

(I also asked this in MathOverflow) I'm looking for a proof of the Local Deduction Theorem for any one of many logics. That is, a proof of the statement: $\Sigma \bigcup \{\phi\} \models \psi$ iff for ...
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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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1 vote
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### " Logic does not allow you to say this": is this assertion outdated?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 ...
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### Expansion postulates in Belief revision logic

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 $\mathcal{L}_0$...
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The expression(~p or p )is a Tautology. Consider this statement(p): This statement is false. Now here, Statement p is paradoxical. My question is :- Can we define paradoxes like this as statements ...
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### Motivations for using Strong-K3 in Sentential Logic.

What motivations might one have for choosing a Strong-K3 interpretation in sentential logic (over other three-valued logics). I'm looking at the functional outputs of each of the connectives on L3, ...
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### Lukasiewicz logic, deduction theorem and complete calculi

3-valued Lukasiewicz logics is known to lack a “semantical" deduction theorem, i.e. $$A\vDash B\not\Leftrightarrow\vDash A\supset B$$ if we define $A\vDash B$ as $\forall v(v(A)=1\Rightarrow v(B)=1)$ ...
1 vote
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### Downward Lowenheim-Skolem-Tarski theorem for Cofinality logic

I was trying to find the precise and strongest statement of the Downward Lowenheim-Skolem-Tarski theorem for Cofinality logic $\mathcal{L}(Q^{cf}_\lambda)$- first order logic enhanced with the ...
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### Is minimal logic equivalent to intuitionistic?

Is minimal logic equivalent to intuitionistic? Obviously this is false if we interpret the symbol $\bot_M$ from minimal logic as meaning the same thing as the symbol $\bot_I$ of intuitionistic logic. ...
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### 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). ...
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### Why there is no classification theorem for logics, if there are classification theorems for groups and algebras?

Why there is no classification theorem for logics, if there are classification theorems for groups and algebras? Why the logics are different, if there are connections between logics and category ...
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### How can we interpret that $A, B \vdash A, B$ is unprovable with resource interpretation in Linear Logic?

In Linear logic (LL), it is unprovable but when considering the resource interpretation it seems to me that from the resources $A, B$ we can produce the resources $A, B$. By $A, B \vdash A, B$ I mean ...
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### Fully truth-functional version of modal logic?

Though the 'square' and 'rhombus' operators from modal logic are not truth-functional, it's because modal logic is interpreted as a binary logic, isn't it? What if modal logic is considered many-...
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### Are there logics without modus ponens?

The question doesn't go beyond the title. And I don't mean logics that merely just don't have it as a primitive rule - I'm interested in logic where you can't actually use it. I've searched around ...
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### Continuous vs classical structures (2)

I am moving my first steps in continuous model theory (tl;dr). This is one of two soft questions on the relation between a continuous and a classical structure. Let $M$ be a classical first-order ...
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### Continuous vs classical structures (1)

I am moving my first steps in continuous model theory (tl;dr). This is one of two soft questions on the relation between a continuous and a classical structure. What can be said about continuous ...
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### 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 ...
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### Free Logic; what is the relation between 'Fa' and ' □Fa'?

I am reading Rod Girle's Modal Logics Philosophy section 8.6 on Free Logic. And I have a problem understanding how truth values of modal logic formulas are determined in free logic. In Rod Girle's ...
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### Free Logic; how to make (∃x)(a ≠ x) (n) true?

I am reading Rod Girle's Modal Logics and Philosophy. And I have a problem with one of the answers of the exercises. In the exercise question, the reader has to provide a counterexample showing the ...