218,481 research outputs found
Matching Logic
This paper presents matching logic, a first-order logic (FOL) variant for
specifying and reasoning about structure by means of patterns and pattern
matching. Its sentences, the patterns, are constructed using variables,
symbols, connectives and quantifiers, but no difference is made between
function and predicate symbols. In models, a pattern evaluates into a power-set
domain (the set of values that match it), in contrast to FOL where functions
and predicates map into a regular domain. Matching logic uniformly generalizes
several logical frameworks important for program analysis, such as:
propositional logic, algebraic specification, FOL with equality, modal logic,
and separation logic. Patterns can specify separation requirements at any level
in any program configuration, not only in the heaps or stores, without any
special logical constructs for that: the very nature of pattern matching is
that if two structures are matched as part of a pattern, then they can only be
spatially separated. Like FOL, matching logic can also be translated into pure
predicate logic with equality, at the same time admitting its own sound and
complete proof system. A practical aspect of matching logic is that FOL
reasoning with equality remains sound, so off-the-shelf provers and SMT solvers
can be used for matching logic reasoning. Matching logic is particularly
well-suited for reasoning about programs in programming languages that have an
operational semantics, but it is not limited to this
Rigidity of amalgamated free products in measure equivalence
A discrete countable group \Gamma is said to be ME rigid if any discrete
countable group that is measure equivalent to \Gamma is virtually isomorphic to
\Gamma. In this paper, we construct ME rigid groups by amalgamating two groups
satisfying rigidity in a sense of measure equivalence. A class of amalgamated
free products is introduced, and discrete countable groups which are measure
equivalent to a group in that class are investigated.Comment: 51 pages, Theorem 1.5 (a) and Proposition 9.5 modifie
Unbounded symmetric operators in -homology and the Baum-Connes Conjecture
Using the unbounded picture of analytical K-homology, we associate a
well-defined K-homology class to an unbounded symmetric operator satisfying
certain mild technical conditions. We also establish an ``addition formula''
for the Dirac operator on the circle and for the Dolbeault operator on closed
surfaces. Two proofs are provided, one using topology and the other one,
surprisingly involved, sticking to analysis, on the basis of the previous
result. As a second application, we construct, in a purely analytical language,
various homomorphisms linking the homology of a group in low degree, the
K-homology of its classifying space and the analytic K-theory of its
C^*-algebra, in close connection with the Baum-Connes assembly map. For groups
classified by a 2-complex, this allows to reformulate the Baum-Connes
Conjecture.Comment: 42 pages, 3 figure
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