Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [predicate-logic]

Questions concerning predicate calculus, i.e. the logic of quantifiers.

Some well-known formal systems covered by this term are

  • first-order logic, containing the quantifiers $\forall$ and $\exists$
  • second-order logic
  • many-sorted logic
  • infinitary logic
4144 questions
0
votes
1 answer

Equality of nested quantified proposition

Say, Q(x,y) is a statement "x has sent a message to y" where the domain for both x and y consists of all students in my class. Is ∀x∃yQ(x,y) the same as ∃y∀xQ(x,y) ? The translation for the former one should be: "Every student in my class has…
Teddy Hartanto
  • 103
0
votes
1 answer

Supervaluational semantic equivalence

I'm working on Ted Siders Logic for Philosophers and I'm stuck on exercise 3.15. I need to show the global and local definitions of supervaluational semantic consequence are equivalent. How do I go about getting started on this?
James
  • 21
0
votes
1 answer

Relation in mathematical logic vs Relation in Sets

When we talk about relations in context of mathematical logic, they are predicates that are contained in the signature of a certain language. For example the signature of ordered fields is: $$\sigma=\{+,\times,0,1, > \}$$ Where $+,\times,0,1,$ are…
steakexchange
  • 231
0
votes
3 answers

What is the difference between these two statements?

I was asked in a course of mine to construct a set where only one of the following statements holds. The statements are: a) For every yellow number a there is a blue number b such that $a
Oscar Flores
  • 1,438
  • 2
  • 18
  • 26
0
votes
1 answer

Finding the sub formula.

Lets say I have the sentence $$\phi=(p(x)\wedge(q(y)\supset R(z))) \supset (\forall u.\exists w.(T(u.w) \vee \neg(u=w)))$$ I am trying to find the sub formulae of this. Is $$(\forall u.\exists w.(T(u.w) \vee \neg(u=w)))$$ a sub formula? In the…
user204450
0
votes
0 answers

Logic: Predicate P(x,y) with only one defined parameter?

I have a question about well-formed/well-defined predicates. Our class was presented with the following exercise: Let ${S}$ denote the set of all students in your class, ${C}$ denotes the set of all countries, and $T(x, y)$ denotes that $x$…
kldv
  • 1
0
votes
1 answer

Transforming structures into logic

Does anyone have any good examples or know where I could find examples of transforming simple structures from graph theory into predicate logic?
user204450
0
votes
1 answer

Defining suitable predicate and function symbols.

I am really struggling to build intuition with regards to how to do this sort of question. The abstract: A graph is a set (whose elements are called nodes) together with a symmetric relation on that set (related nodes are said to have an edge…
user204450
0
votes
1 answer

Valuations and logic

I have been given the question Let $$Var=\{x,y,z\}$$ $$ U=\{0,1,2\}$$ $$I(p)=\{(0,1),(1,2)\}$$ Give a valuation so that P(x,y) is true? What is a valuation? I do not understand it intuitively. Also what does I(p) mean?
user204450
0
votes
1 answer

Truth of sentences

Let say I have a signature $\{ P_1^1 ,P_2 ^2 , F^2 \}$ with the interpretation $$U= \{ 0,1 \}$$ $$R_1= \{ 0 \}$$ $$R_2= \{ (0,1),(1,0) \}$$ $$F={(0,0,1),(1,0,0),(0,1,0),(1,1,1)}$$ I have been given a sentence $$\exists x.P_1 (x)$$ Why is this…
user204450
0
votes
1 answer

If $P$ is a predicate symbol with arity $1$, why is $P(x)$ not a term?

If $P$ is a predicate symbol with arity $1$, why is $P(x)$ not a term? Is it because terms can only consist of function symbols applied to variables? i.e $F(x)$ where $F$ is a function symbol of arity $1$ and $x$ is a variable.
user99865
0
votes
1 answer

Give counterexample for $\forall x (P(x) \rightarrow Q(x)), \exists x(P(x)) \vdash \forall xQ(x)$

I know this should be quite easy but I can't figure out how I have to write down a model as a counterexample for this: $\forall x (P(x) \rightarrow Q(x)), \exists x(P(x)) \vdash \forall xQ(x)$ Let's say $ P = \{ \text{students who attended exam…
Stefan Falk
  • 1,217
  • 1
  • 11
  • 24
-1
votes
1 answer

How to convert a sentence into first order logic?

There is a student who does not like punctual students. Where, S(x) = “x is student” P(x) = “x is always punctual” L(x, y) = “x likes y” can please help me? Thanks Alot~~
MAINAME KC
  • 1
-1
votes
1 answer

Symbolizing the expression: "All the world loves a lover".

In the book Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar, there's an example question in the section on Predicate Calculus. Symbolize the expression "All the world loves a lover". My…
Masked Man
  • 233
-1
votes
1 answer

free variable predicate logic

I'm trying to understand the concept of free variables in predicate logic. To my understanding, in the equation: ∃x.∀y.x ≥ y x is not a free variable (it is bound) since it is within the scope of ∃x
user1068052
1 2 3
…
22 23