Questions tagged [algebraic-logic]
Use this tag for questions related to reasoning obtained by manipulating equations with free variables.
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Does every variety of locally finite closure algebras have a unification type?
An algebra has one of four unification types - unitary, finitary, infinitary or nullary. A variety $\mathbf{V}$ has type unary, if every member has unary type, finitary, if every member has finitary ...
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Prove that $A' ∪ B' ∪ (A ∩ B ∩ C')$ is equivalent to $A' ∪ B' ∪ C'$ by algebraic laws
I know $A' ∪ B' ∪ (A ∩ B ∩ C')$ is equivalent to $A' ∪ B' ∪ C'$ by drawing Venn diagram.
But I can't successfully prove by algebraic laws.
Here is what I've tried:
$$A' ∪ B' ∪ (A ∩ B ∩ C')$$
$$= A' ∪ [...
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Subset Inequality Problem
Here’s a problem I have been looking at recently. I’m looking for feedback, references, and/or solutions. Thanks. FGS 3.13.23.
Given
A set $X$ of $6$ natural numbers $X = \{X_1, X_2, X_3, X_4, ...
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Relation algebras and quantifier rank
On the Wikipedia page for relation algebra (RA), one encounters the following peculiar fact (see section Expressive power):
"RA can express any (and up to logical equivalence, exactly the) first-...
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Relationship between measure theory and quantification
In a 1978 paper published by David P. Ellerman and Gian-Carlo Rota, the duo discuss the relationship(s) exhibited by measure theory, probability theory, and logic paying special attention to how these ...
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Weakening of projectivity for Boolean algebras independent from projectivity
We say that a Boolean algebra $B$ is projective if for all Boolean algebras $C$ and $D$, if $f:C\to D$ is an onto homomorphism, and $g:B\to D$ is any homomorphism, there is some homomorphism $h:B\to C$...
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Equational axioms for quantifiers
I seek an equational axiomatization of the quantifiers of predicate logic (that permits empty domains).
Start with the equational axioms for Boolean algebra. Add the following axioms, which come in ...
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Transfer between different signatures of the same logic
I'm formalising parts of modal, intuitionistic and classical logic in Coq. So I have to keep track of nitty-gritty details.
To simplify proofs that use the syntax, I'd like to use the signature $\...
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Formal proof for a syllogism
Let $p(x),q(x),r(x)$ unary predicates in some language. Consider the deduction
$$\exists x (p(x) \land q(x) ), \forall x (q(x) \rightarrow r(x)) \vdash\exists x (p(x) \land r(x))$$
I want to find a ...
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What is connection between Group theory and Logic?
I have just started to study Algebraic logic.
What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of ...
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Is there work on constructive interpretations of algebraic logic?
Variables are finicky. I've been looking at algebraizations of first-order logic recently to figure things out in more detail. Mostly I've been looking at Tarski's Cylindrical algebra but lately I ...
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Boolean valued models in a general setting
It is well known that Boolean valued models play significant roles for set-theoretic purposes. But how well-studied are Boolean valued models in a more general setting, as models for random first-...
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A fact about algebraic systems and axiom of choice
Algebraic system $\mathfrak A$ contains a proper subsystem $\mathfrak B$ isomorphic to $\mathfrak A$. Prove that $\mathfrak A$ is contained in a proper supersystem $\mathfrak C$ isomorphic to $\...
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What flavours of Linear Logic are algebraizable?
I am a theoretical linguistics student and I have been working in the last few years on an improved model of natural language semantics, but I am missing a final mathematical insight in order to wrap ...
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A structure with controlled commutativity as a model of logical calculi
I've discovered a parametric structure that can be used to create models of certain logical systems. The idea is simple, so I'm probably not the first one to invent it. Please help me identify the ...
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