Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Expressive Power of k-ary Exclusion Logic   In this paper we study the expressive power of k-ary exclusion logic, EXC[k],
that is obtained by extending first order logic with k-ary exclusion atoms. It
is known that without arity bounds exclusion logic is equivalent with
dependence logic. By observing the translations, we see that the expressive
power of EXC[k] lies in between k-ary and (k+1)-ary dependence logics. We will
show that, at least in the case of k=1, the both of these inclusions are
proper.
  In a recent work by the author it was shown that k-ary inclusion-exclusion
logic is equivalent with k-ary existential second order logic, ESO[k]. We will
show that, on the level of sentences, it is possible to simulate inclusion
atoms with exclusion atoms, and this way express ESO[k]-sentences by using only
k-ary exclusion atoms. For this translation we also need to introduce a novel
method for "unifying" the values of certain variables in a team. As a
consequence, EXC[k] captures ESO[k] on the level of sentences, and we get a
strict arity hierarchy for exclusion logic. It also follows that k-ary
inclusion logic is strictly weaker than EXC[k].
  Finally we will use similar techniques to formulate a translation from ESO[k]
to k-ary inclusion logic with strict semantics. Consequently, for any arity
fragment of inclusion logic, strict semantics is more expressive than lax
semantics.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio