Written work: The following problems are SUGGESTED for practice (they could be on the final!), but will NOT be collected.
Sec 12.6 p216: 1, 2
Sec 13.1 p222: 1, 4, 5
WeBWorK – none
OpenLab – none
Project Reflection – Due before the final exam, Tuesday 12/19.
Handy Links
Logic on Math StackExchange
- Finite axiomatization of EFA June 26, 2024According to the paper Fragments of Peano's Arithmetic and the MRDP theorem (Section 6), elementary function arithmetic (EFA) is finitely axiomatizable. Is there a known explicite finite axiomatization? If not, what is an upper bound on the number of axioms needed?Anserin
- Finding the group of all models for predefined sets June 26, 2024Given a set of theorems $T$, define $M(T)$ to be a set containing all models of $T$. A set of assignments $K$ is called "Hedgeable" if exists a set of theorems $T$ s.t. $M(T)=K$, otherwise K is non-hedgeable. How (and what does it mean) can i find $M(T)$ for the following sets: $$ T_1=\{All\ \ […]Aishgadol
- Equational theory in the language of rings with no known equational proof June 26, 2024I'm interested in equational logic which is the fragment of classical logic with only $\forall$ and $=$ as logical symbols and nothing else. In contrast with the logic described in the Wikipedia article, I disallow $\varphi \leftrightarrow \psi$ where $\varphi$ and $\psi$ are both propositions, despite the obvious analogy between $\leftrightarrow$ and $=$. I'm mostly […]Greg Nisbet
- How to extend the $p \Rightarrow q$ constraint with logical AND within the $p$ statement for Big-M method? June 25, 2024I am a network engineer who is currently doing some network optimization problem. In my application, there is a requirement for the network delay to be bounded in some interval once some boolean flag is triggered. Particularly, it is of the form $x = 1 \Rightarrow a \le u \le b$. Here $x,u$ are the […]Tuong Nguyen Minh
- Measuring and comparing impact June 25, 2024I want to measure the impact of mentoring. I am writing to ask if calculating percent increase is an appropriate use to make a comparison. I’m using survey data on job satisfaction. In addition, respondents have indicated if: 1. they don’t have a mentor, 2. if they have an informal mentor, or 3. if they […]Kelly
- How do I solve the exercise 2.2.5 (a) from Modal Logic? June 25, 2024It provides me with two models M0=(R,Hannibal-Barca Yang
- Is truth value the only type of value which can be logically preserved by means of semantic consequence? [closed] June 24, 2024Is a formal system of semantic consequence (as opposed to syntactic consequence) with a value having nothing to do with truth possible? I'm not here interested in n-valued logics which include truth and falsity, (for example, a four-valued logic with the possible values of true, false, both, and neither).FreeThought
- Is it possible to deduce $\vdash \psi$ from $\{\varphi\}\vdash \psi$ and $\{\neg \varphi\}\vdash \psi$ in fuzzy logic? June 24, 2024Assume we are in Basic Logic introduced in here (fuzzy logic), and we have $\{\varphi\}\vdash \psi$, and $\{\neg \varphi\}\vdash \psi$. Can we conclude that we have $\vdash \psi$? Or do we have to provide a proof? Can I consider it as obvious? If we have to prove it, where should I start?Doralisa
- Given a strong enough theory, why is $\operatorname{Richardian}(n)$ ill-defined? June 24, 2024Richard's paradox (on natural numbers) can be summarized as follows: Let $R$ be an enumeration of all the possible unary predicates that can apply to natural numbers. Perhaps, for example, $R_1(n) := n\text{ is even}$, $R_2(n) := n\text{ is odd}$, $R_3(n) := n\text { is prime}$, $...$, $R_{53}(n) := \exists m : n^2 = 3m […]Feryll
- Proof of bijection between $S_1(R,\underline{R})$ and the set of cuts in $(R,<)$ June 24, 2024Hi guys I am trying to solve the following exercise but without great success and I hope you can help me: "Let $\underline{R}$ be a real closed field (RCF). Show that $S_1(R,\underline{R})$ is in one to one correspondence with the set of cuts in $(R,WiggedFern936
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