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3
votes
0answers
33 views

Substitution in Resolution Proofs

Let $F = C_1 \wedge C_2\; \wedge ... \wedge\; C_m$ be a unsatisfiable $k$-CNF on variables $x_1,...,x_n$, where $k$ is constant. Let $x_j\rightarrow x_j^1\wedge x_j^2$ be a substitution that replaces ...
-3
votes
1answer
174 views

“tree-like” vs “DAG-like” resolution

hi all there seems to be a deep/not-much-explored phenomenon in the way that SAT resolution proofs can define a tree and/or a DAG & its relationship to lower bounds/circuit complexity. could there ...
2
votes
0answers
153 views

Most general form of SAT which is in P

2-SAT is in P. Additionally, a (CNF) SAT-problem is trivially poly-time solvable if no two expressions can be resolved (via Robinson resolution, ie for every pair of disjunctive clauses, they either ...
1
vote
1answer
187 views

What is resolution ((in FOL))? [closed]

I'm searching for an authoritative definition of resolution (logic resolution). Preferably on a reference freely available on the Internet (so I can read it right now). If this is too broad then ...
1
vote
1answer
93 views

Implied Clause and Resolvent

(I posted this question on MathSE first, no answer, that is the reason why I come here.) Let $F$ be a 3-CNF formula on $n$ variables. A clause $c$ is implied by the formula if $F$ and $F \wedge c$ ...
3
votes
1answer
135 views

About Closure under Resolution

The question looks very simple, that is why I posted it first on MathSE, unsuccesfully - no answer for 12 days. I tried to find a short and elegant answer to the question, but I haven't succeed yet. ...
12
votes
2answers
914 views

Is propositional resolution a complete proof system?

This question is about propositional logic and all occurrences of "resolution" should be read as "propositional resolution". This question is something extremely basic but it has been bothering me ...