Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequential operators in computability logic   Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a
semantical platform and research program for redeveloping logic as a formal
theory of computability, as opposed to the formal theory of truth which it has
more traditionally been. Formulas in CL stand for (interactive) computational
problems, understood as games between a machine and its environment; logical
operators represent operations on such entities; and "truth" is understood as
existence of an effective solution, i.e., of an algorithmic winning strategy.
  The formalism of CL is open-ended, and may undergo series of extensions as
the study of the subject advances. The main groups of operators on which CL has
been focused so far are the parallel, choice, branching, and blind operators.
The present paper introduces a new important group of operators, called
sequential. The latter come in the form of sequential conjunction and
disjunction, sequential quantifiers, and sequential recurrences. As the name
may suggest, the algorithmic intuitions associated with this group are those of
sequential computations, as opposed to the intuitions of parallel computations
associated with the parallel group of operations: playing a sequential
combination of games means playing its components in a sequential fashion, one
after one.
  The main technical result of the present paper is a sound and complete
axiomatization of the propositional fragment of computability logic whose
vocabulary, together with negation, includes all three -- parallel, choice and
sequential -- sorts of conjunction and disjunction. An extension of this result
to the first-order level is also outlined.

14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph