Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Axiomatic constraint systems for proof search modulo theories   Goal-directed proof search in first-order logic uses meta-variables to delay
the choice of witnesses; substitutions for such variables are produced when
closing proof-tree branches, using first-order unification or a theory-specific
background reasoner. This paper investigates a generalisation of such
mechanisms whereby theory-specific constraints are produced instead of
substitutions. In order to design modular proof-search procedures over such
mechanisms, we provide a sequent calculus with meta-variables, which
manipulates such constraints abstractly. Proving soundness and completeness of
the calculus leads to an axiomatisation that identifies the conditions under
which abstract constraints can be generated and propagated in the same way
unifiers usually are. We then extract from our abstract framework a component
interface and a specification for concrete implementations of background
reasoners.

4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
9
The categories of this paper are: nlin