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Logic on Math StackExchange
- Is there a logic system where the information entropy of a formula determines anything that has to do with the said formula? May 20, 2025Just like the question says. I tried to find if the information theory in general plays a significance in any logical system in general but couldn't find anything. More detailedly, maybe the information entropy of a formula determines a "local" inference rule posed on it, like how it can be transformed to another formula besides […]ohiosigmarizzler
- How can I visually represent the preference ranking in a cumulative system C? [closed] May 20, 2025I want to represent with a graph the way the cumulative system C (by KLM) organizes its preferences. I have three proposition, a>b>c. I want to represent how the combination of their values (1,0) may be represented in a graph, with the totality of them true as best case scenario and the their being 0 […]beazpanofsky
- Semantic entailment and semantic tableaux [duplicate] May 20, 2025I'm trying to understand the difference between semantic and syntactic entailment. While I think I have understood the differences, the concept of semantic tableaux puzzled me. At first, I thought they were a tool to prove semantic entailment. However as I kept reading, it became clear that they are syntactic tool and not semantic one. […]Luciano Robino
- $∀x\ L(x, y)$, where the universe is the set of all people, and $L(x, y)$ means “$x$ likes $y$" is this statement's truth dependent on variable "y"? [duplicate] May 19, 2025The statement, $∀x\ L(x, y)$, where the universe is the set of all people, and $L(x, y)$ means “$x$ likes $y$", clearly implies that y is liked by each $x$ for all $x$ that exists in the set/ universe. So should it really matter what $y$ is? Since it's liked by all the $x$, it […]Soham Patil
- Why isn't the syntax of logic constrained to only include semantically closed (meaningful) formulas? [closed] May 19, 2025In standard first-order logic (and similarly in modal logic), the formation rules allow for the construction of formulas like $x = x$ or $p$, even though these expressions are not truth-evaluable without further context — namely, an assignment for $x$, or a modal framework for $p$. This strikes me as conceptually problematic. Why allow the […]Daniel Lü
- Is it necessary to prove that a set is non-empty before discussing properties of its elements? May 18, 2025In mathematical arguments, especially those involving existence claims, is it necessary to first establish that a set is non-empty before discussing the properties of its elements? For example, suppose someone claims, "There may exist a number with a certain property P." From a formal logic or mathematical standpoint, should one first demonstrate that the set […]Abu Alimah
- Putting parameterized subtheories within a larger theory [closed] May 17, 2025I have a first order language $L$ consisting of a binary relation symbol $\leq$, a monary function symbol $f$, and a few constants. Let $\{T_n\}_{n\in \mathbb{N}}$ be a set of theories in $L$. They are infinite, but aren't too complicated and mainly just specify that $\leq$ is a total linear ordering, plus some not too […]Adam
- Given a model with a specific property find another elementarily equivalent to it May 17, 2025Let $\mathcal{L}=\{Bañó
- When does an ontology-mutating proof-search chain almost surely invent a novel theory? [closed] May 16, 2025In a previous post I asked whether the composite kernel $$K = (1-\alpha-\beta)M_{\text{low}} + \alpha M_{\text{high}} + \beta M_{\text{ax}}, \quad 0user1632355
- Irreducibility of multi-level proof-mutation kernels May 16, 2025The recent AlphaEvolve white-paper shows how an evolutionary loop over token-level “diffs’’ can discover novel programs (which translates to novel mathematical solutions/objects based on a quality measure). Inspired by that framework, consider a proof-search analogue inside Lean. A state is a string that serialises the current proof script together with its open goals. Three stochastic […]user1632355
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