Questions tagged [propositional-logic]
208 questions
25
votes
7 answers
Why is A implies B true if A is false and B is false?
It seems to me that the 'implies' in English language does not mean the same thing as the logical operator 'implies', in a similar way how 'OR' word in most cases means 'Exclusive OR' in our everyday language use.
Let's take two examples:
If today…
yoyo_fun
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22
votes
11 answers
Why is $A \lor (A \land \neg B) \equiv A$?
I would like to know if there is a rule to prove this. For example, if I use the distributive law I will get only $(A \lor A) \land (A \lor \neg B)$.
user78333
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19
votes
4 answers
Can proof by contradiction work without the law of excluded middle?
I was recently thinking about the validity of proof by contradiction. I’ve read for the past few days things on intuitionistic logic and Godel’s theorems to see if they would provide me answers to my questions. Right now I still have questions…
Charlie Parker
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13
votes
5 answers
Why does soundness imply consistency?
I was reading the question Consistency and completeness imply soundness? and the first statement in it says:
I understand that soundness implies consistency.
Which I was quite puzzled about because I thought soundness was a weaker statement than…
Charlie Parker
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9
votes
2 answers
How is implication same as entailment
In propositional logic (Artificial intelligence to be specific) $\alpha$ entails $\beta$ iff $\alpha\Rightarrow\beta$ is a statement.
However if I write the truth table for implies ($\Rightarrow$) if $\alpha$ is false implies that $\beta$ is a true…
Abhishek Dhankar
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7
votes
4 answers
Boolean algebraic expression vs Propositional logic expression
There is a lot of similarity between Propositional logic and Boolean algebraic expressions.
Similar aspects :
1) Both has variables of two states.
2) Operations of Boolean algebra and propositional logic are similar.
3) Simplification of formula…
hanugm
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6
votes
1 answer
What is the connection between combinatorial circuits and finite state automata?
The diagram on the Wikipedia page of FSA shows the hierarchy of the computational devices, in that diagram it is denoted that the finite state machines are superior to the combinatorial circuits.
Combinatorial circuits are the model of propositional…
Jayendra Parmar
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6
votes
1 answer
Implementing mathematical theory of arithmetic in Haskell via Curry-Howard correspondence
I have to ask for forgiveness in advance if the whole question doesn't
make a lot of sense, but unfortunately, I have no better intuition as
of right now and this seems like the best starting point I could come
up with.
I'm reading Tarski's book…
Kostiantyn Rybnikov
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6
votes
2 answers
Operator precedence in propositional logic
there is some kind of priorities for the elements in propositional logic ?
for example : p ∧¬q → r , given this ,we there may be two options
(p ∧¬q) → r OR p ∧ (¬q → r) , which one is the correct ?
Roberto Fernandez Diaz
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5
votes
2 answers
Why algorithms calculating non-tirivial zeros can't be used as proofs of Riemann Hypothesis?
Recently I was reading again this propositions as types paper by Philip Wadler:
http://homepages.inf.ed.ac.uk/wadler/papers/propositions-as-types/propositions-as-types.pdf
It gives an impression, that programs are proofs. So my first question was…
MarkokraM
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5
votes
2 answers
How to read out a double negation in propositional logic
How would one verbally say ~~R where R = my program is correct? The tildes are negation symbols. I'm not sure if it just cancels out and comes out as 'my program is correct' or if it's something else.
Thank you!
Kye
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5
votes
1 answer
How to find a minimum set of axioms within a set of propositions?
I have a set of propositions, for example $\{a_1,a_2,\dots,a_n\}$. Some propositions depend on others (for example, $a_1,a_2\Rightarrow a_3$, means if $a_1,a_2$ are true, then $a_3$ is true). I want to find a subset of the propositions to be defined…
maple
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5
votes
3 answers
Find hamilton cycle in a directed graph reduced to sat problem
I need to find a Hamiltonian cycle in a directed graph using propositional logic, and to solve it by sat solver. So after I couldn't find a working solution, I found a paper that describes how to construct a CNF formula to find an Hamiltonian…
Dor Cohen
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5
votes
2 answers
P, Q, ((P→Q)→R) ⊢ R using only modus ponens
Can $R$ be inferred from $P$, $Q$, and $(P \to Q) \to R$ using only modus ponens?
My understanding is that it can, as shown below, but I was told this was incorrect.
Proof of ${P, Q, (P \to Q) \to R} \vdash R$ using modus ponens:
P, Q, (P->Q)->R :…
Max Burns
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4
votes
1 answer
Knight and knaves
I have these in my lecture notes, its about the rules where knights always tell the truth and knaves always lie:
If A says “The statement ‘there is gold on the island’ and the statement ‘I am a knight’ are either both true or both false” he is…
Astoach
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