Commit 4787b821 authored by Martin Jonas's avatar Martin Jonas
Browse files

Polishing

parent cc7d22bb
......@@ -85,7 +85,7 @@ and to each predicate symbol $P \in \Sigma^p$ of arity $n$ assigns a
relation $P^\mathcal{A} \subseteq A^n$. Given a $\Sigma$-structure
$\mathcal{A}$, there exists a unique homomorphic extension of
$(\_)^\mathcal{A}$ to $\Sigma$-terms, which to each $\Sigma$-term $t$
assigns an element $t^\mathcal{A} \in A$. In turn, using standard
assigns an element $t^\mathcal{A} \in A$. In turn, by using standard
definitions, the assignment $(\_)^\mathcal{A}$ can be further extended
to assign a truth value $\varphi^\mathcal{A} \in \{ \true, \false \}$
to each $\Sigma$-formula $\varphi$. A $\Sigma$-structure $\mathcal{A}$
......@@ -159,9 +159,9 @@ signature, defined in the previous subsection, a \emph{many-sorted
modified. Arity of a symbol determines not only a number of its
arguments, but also their types -- each function symbol has assigned
$(n+1)$-tuple of sort symbols for a non-negative integer $n$ and each
predicate symbols has assigned a $n$-tuple of sort symbols for a
predicate symbol has assigned a $n$-tuple of sort symbols for a
non-negative integer $n$. Simultaneous inductive definition of terms
of a sort $S \in \Sigma^S$ and definitions of atoms, literals, clauses
of sorts $S \in \Sigma^S$ and definitions of atoms, literals, clauses
and formulas are straightforward and can be found for example in
Enderton~\cite{End01}.
......@@ -204,7 +204,7 @@ the other hand, if after elimination of all variables no clauses
remain, the formula is satisfiable. The main problem of \dppr is its
space complexity, since the number of the clauses may grow
exponentially even for simple formulas. To alleviate this problem, the
refinement of \dppr algorithm was introduced in 1962 by Davis,
refinement of the \dppr algorithm was introduced in 1962 by Davis,
Logemann and Loveland~\cite{DPLL62}.
The Davis--Putnam--Logemann--Loveland \quotegraffito{If you don't know
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment