# 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.

67 questions
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### “ Logic does not allow you to say this”: is this assertion outdated?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 ...
1answer
100 views

### 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 ...
1answer
39 views

### 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 $\mathcal{L}_0$...
0answers
33 views

### Can temporal logic be included in the framework of modal logics K, 4, D, T? Substructural temporal logic?

I am reading the article "A uniform framework for substructural logics with modalities" https://easychair.org/publications/paper/d5zT which gives impression that K, 4, D, T (and some possible ...
2answers
134 views

### Paradox vs Tautology.

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 ...
1answer
45 views

### 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, ...
1answer
156 views

### 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 $\forall v(v(A)=1\Rightarrow v(B)=1)$ ...
0answers
38 views

### 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 ...
1answer
196 views

### 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. ...
1answer
426 views

### 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). ...
1answer
89 views

### 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 ...
1answer
85 views

### 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 ...
2answers
476 views

### 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 ...
0answers
40 views

### 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 ...
1answer
68 views

### 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 ...
0answers
305 views

### 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 ...
0answers
70 views

### 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 ...
1answer
61 views

### 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 ...
1answer
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### Conditions for total orders in temporal logic

Let $(T,>)$ be a frame of minimal temporal logic, i.e. a frame as defined in Kripke semantics where the relation is a partial order relation $>$ defined on the set $T$ of worlds, called instants....
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39 views

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### Symmetric relations and $\varphi\rightarrow\square\diamond\varphi$

I read that the schema $$\varphi\rightarrow\square\diamond\varphi$$ corresponds to the symmetric property (D. Palladino, C. Palladino, Logiche non classiche, 'non-classical logics', 2007) of the ...
1answer
443 views

### Euclidean relations and $\diamond P\rightarrow\square\diamond P$

I read* that the formula $$\diamond \varphi\rightarrow\square\diamond\varphi$$is valid in a structure $(W,R)$, intended as in Kripke semantics, -i.e. that it is true for any interpretation $I$ and in ...
2answers
291 views

1answer
539 views

### What are some practical applications of mathematical/formal logic to science and humanities? [closed]

I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very self facing, with logicians proving things for other logicians. It left me ...