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Questions tagged [fitch]

Frederic Brenton Fitch (1908 – 1987) was an American logician who taught at Yale. He invented the Fitch-style for natural deduction. He is also famous for the paradox of knowability. The tag may also refer to natural deduction proof environments in Fitch-style calculus for giving and checking proofs.

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How to prove H → M ¬H → ¬M prove H↔M?

I'm using the program Fitch and I need to make a formal proof for this: H → M ¬H → ¬M Prove: H↔M Any ideas on how to do so?
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4answers
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Language Proof & Logic 8.31 Fitch Proof

Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
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1answer
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How can I prove the law of excluded third (p ∨ ¬p)) using Fitch?

Good day. I do not quite understand how I can get ~~p after the 11th line. According to the proof of the law itself (and all reasonable logic) I should get it, and then simplify the expression - but ...
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how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

I am totally lost on how to do this... can anyone help? What does it mean? I tried to understand what it means before proof but am totally clueless
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1answer
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Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...
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1answer
262 views

Language, Proof, and Logic 14.11 Fitch Proof

Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
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2answers
151 views

Language Proof and logic Chapter 13 problem 31

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. I don't see how this is supposed to work out Here are the premises: ∀x ∀y[Likes(x,...
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Fitch Proof Exercise 6.20

I am working on a proof and am stuck on a step. I am not sure why I cannot assume the negation of B. Is it not allowed or am I missing something? Thank you]1
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Fitch Proof Help

I'm having some trouble solving this proof in Fitch. How do the universals switch place from the premise to the goal? There is no negation in the goal so negation introduction is not the way to go, I ...
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2answers
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Fitch Questions Please Help Me

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
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3answers
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In Fitch, how does one prove “(P → Q)” from the premise “(¬P ∨ Q)”?

It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck. I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
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How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
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2answers
156 views

Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
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1answer
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De Morgan's Law Formal Proof [duplicate]

Does anyone know how to do this without the use of addition rules? We have not covered that in class, and all the info I can find online suggests that as a solution. Thanks]1
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1answer
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Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
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4answers
279 views

In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)

Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R) I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
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2answers
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How to use use the Fitch System to prove (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q) ⇒ p)?

I'm getting a bit stuck in a tailspin on this one. I'm quite new to logic. I'm not sure how or when we use negation to get P. How then does that connect to (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q)?
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Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
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2answers
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Given premise ~(P↔Q) how can one derive (~P↔Q) using Fitch?

Given premise ~(P↔Q) derive (~P↔Q) using Fitch-style natural deduction. I thought of simplifying the premise but I am still not able to find an answer. Can someone please help me?
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1answer
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How do you prove (p => q => r) => (p => q) => p => r using the Fitch system?

I'm quite new to logic. Thank you for taking the time to review this post. I tried the following and got to the conclusion I wanted but I was never able to prove the statement.
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1answer
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Fitch Proof - Arrow's logic of preferences

I've been stumped on this one question in particular for several days now and I'm hoping to get some help on where I'm going wrong. Given the following premises: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,...
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1answer
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Fitch Arrow Proofs [closed]

Using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C10 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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3answers
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How do I apply existential elimination to the following Fitch proof?

I am trying to prove ∀x.∀y.loves(x,y) from Relational Proofs using the Fitch system from Barwise and Etchemendy. I can get as far as line 5, but I cannot figure out how to apply Existential ...
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Fitch Question Please Help Me [closed]

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : [![enter image description here][1]][1] How do I reach this goal? Which rules do I use and with which ...
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2answers
83 views

Fitch Question Help

I'm having trouble understanding quantifiers in proofs. The proof I'm working with is : ¬∀x Tet(x) -- Premise ¬∀x (Tet(x) ∧ Medium(x)) -- Goal How do I reach this goal and also get to the goal ...
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1answer
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Conditional IFF - Not sure what's wrong

"Not a valid application of the rule". I don't think 7 - 8 is something that really needs to be proven beyond a reit, but I feel like you should be able to... I'm quite confused on proving Cube(a) ...
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2answers
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Solving a proof in which the goal is the negation of a variable in Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. A ^ B (A ^ ~C) --> ~D A -> ~C (B ^ E) --> (C v D) ~E I ...
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2answers
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Fitch Proof - LPL Exercise 8.17

I am currently finding the third part of this exercise (Conditional 3) difficult to prove. I was sure that my proof was correct, but the Fitch program is saying otherwise. I am finding it ...
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2answers
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Structure of an if and only if proof

I am trying to get this proof to work out and so far I feel like I have the first part right but I'm stuck on how to get the A→B part.
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3answers
364 views

Fitch Proof Question

I'm having trouble with a proof and I'm not sure if it's valid or not. If it appears to be invalid, we are supposed to assign names to the letters in the proof and check it in a World, but when I do ...
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1answer
341 views

How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

How would a formal Fitch proof look like. I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic. I am confused on how to proceed with the proof. Please advice me ...
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2answers
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Fitch-style natural deduction

How to prove the following questions? (a) p from assumption ¬(p → q) (b) ¬¬p → p from no assumptions.
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1answer
286 views

trouble with rules of inference practice problems [closed]

Prove the following symbolized arguments applying the appropriate rules of inference: 1) P ∨ Q = M ⊃ ¬ Q M =conjunction Therefore P 2) (P V Q) ∧ ¬ Q P ⊃ R =...
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4answers
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Symbolic Logic - Quantifier Proof (w/ Conditionals)

I'm not sure if lines 6 - 7 & 8 - 11 are being done correctly. I feel like it's necessary to prove 12 which proves the rest of the problem. I'm a bit stuck on lines 8 - 11. I initially tried to ...
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4answers
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How to prove : (( P → Q ) ∨ ( Q → R )) by natural deduction

Here's another of Tomassi's exercises I can't solve (Logic, page 106): : (( P → Q ) ∨ ( Q → R )) I have to use natural deduction and the only rules I know are: • assumptions, • modus ponendo ...
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3answers
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In Fitch, how does one prove ¬(B ∧ C) from two premises (A → ¬B) and (¬A → ¬C) [closed]

Help me out please!! I have been trying to solve it for hours
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2answers
271 views

Language proof and logic Chapter 15 question 21 how?

I'm really not understanding the set up of how to go about solving this problem any help is welcome
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2answers
218 views

language proof and logic chapter 13 question 49 Help

Premises: ∃xP(x) ∀x∀y((P(x)∧P(y)) → x = y) Prove: ∃x(P(x)∧∀y(P(y) → y = x)) I've started it but the end is starting to get super muddy and not work out and I don't know where I went wrong.
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3answers
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Fitch Proof - Logic LPL 13.11

I am currently doing questions for my course from LPL Chapter 13.11. I have posted the screenshot of what I am trying to do. I am quite stuck and I can not think of a way to get to ~Tet(a). Any hint ...
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1answer
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language logic and proof chapter 12 question 49 and question 50

I've been working on this and I can't seem to figure out what exactly is going wrong can anyone help?
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In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?

I can't figure out how to prove that formally. Please, help!!
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4answers
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How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’

What would a formal Fitch proof for this look like? I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it. I started with this, but I don't know if I am doing the right thing, and where to go ...
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3answers
548 views

2 simple Formal Fitch Proofs

I'm having difficulty proving these. They seem obvious, but I can't figure how to set up formal proofs for them. Could anyone give me clues on how to start them? ¬(P∧¬Q) from the premise P→Q; ¬Q→(R→P)...
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Fitch Proof by Contradiction help

Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question. I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
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2answers
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Disjunctive Syllogism in a Fitch Style System

I'm trying to prove an argument of the form: B ~(C & B) Therefore: ~C. I can expand out ~(C & B) into ~C OR ~B, and with the premise B, it is clear that ~C is the case. ...
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2answers
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Fitch Biconditional Proof Help?

Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
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2answers
121 views

Symbolic Conditional Help

Premise: (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Cube(c) -> Dodec(e) Goal: ~Tet(a) -> Dodec(e) Anyone have a clue on where to start with this?
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2answers
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How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?

I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try. First attempt: Second attempt:
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2answers
430 views

Does rejecting the law of the excluded middle mean rejecting it for all propositions or only for those one cannot derive?

Wikipedia describes the law of the excluded middle as such: In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is ...
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Why does modal logic need to use ◻◻p?

In Frederic Fitch's Symbolic Logic he proves (11.8, page 66) that "◻p" coimplicates "◻◻p". In 11.10 (page 66), he writes, A system almost the same as the system Lewis calls S2 is obtainable by ...