Questions tagged [propositional-logic]

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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 ...
4k views

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 $(A \lor A) \land (A \lor \neg B)$.
6k views

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 ...
3k views

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 ...
6k views

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 ...
2k views

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. ...
408 views

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 ...
3k views

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 ...
532 views

582 views

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. ...
199 views

792 views

Does exist any horn formula that is equisatisfiable to the clause that is disjunction of two literals? Does also exist equivalent?

I just and simply want to know if whether or not exist any horn formula that is equisatisfiable to $(p\lor q)$. I would also be interested to know if there also exists equivalent.
465 views

Why is SAT based on the CNF?

I have been reading up on Boolean logic and, specifically, the Boolean satisfiability problem. I have seen several people mention that the expression must be converted to conjunctive normal form (CNF) ...
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92 views

Are there any techniques for checking whether a clause is subsumed by another clause when adding it to a cnf formula?

When doing variable elimination on a formula in cnf form, there is created a lot of new clauses. Is there any efficient way to check if these are subsumed by other, already existing clauses?
279 views

Does every 3CNF propositional formula has an equivalent 2CNF propositional formula?

Does every 3CNF propositional formula has an equivalent 2CNF propositional formula? Definitions: 3CNF propositional formula is conjunctive normal form propositional formula, which is just ...
607 views

What are the differences between propositional logic and temporal logic?

I am currently studying temporal logic and find it much similar to propositional logic. However, temporal logic seems to be slightly more specific because it encapsulates more precise meaning symbols, ...