458 research outputs found
Elimination of spatial connectives in static spatial logics
AbstractThe recent interest for specification on resources yields so-called spatial logics, that is specification languages offering new forms of reasoning: the local reasoning through the separation of the resource space into two disjoint subspaces, and the contextual reasoning through hypothetical extension of the resource space.We consider two resource models and their related logics:•The static ambient model, proposed as an abstraction of semistructured data (Proc. ESOP’01, Lecture Notes in Computer Science, vol. 2028, Springer, Berlin, 2001, pp. 1–22 (invited paper)) with the static ambient logic (SAL) that was proposed as a request language, both obtained by restricting the mobile ambient calculus (Proc. FOSSACS’98, Lecture Notes in Computer Science, vol. 1378, Springer, Berlin, 1998, pp. 140–155) and logic (Proc. POPL’00, ACM Press, New York, 2000, pp. 365–377) to their purely static aspects.•The memory model and the assertion language of separation logic, both defined in Reynolds (Proc. LICS’02, 2002) for the purpose of the axiomatic semantic of imperative programs manipulating pointers.We raise the questions of the expressiveness and the minimality of these logics. Our main contribution is a minimalisation technique we may apply for these two logics. We moreover show some restrictions of this technique for the extension SAL∀ with universal quantification, and we establish the minimality of the adjunct-free fragment (SALint)
Separability in the Ambient Logic
The \it{Ambient Logic} (AL) has been proposed for expressing properties of
process mobility in the calculus of Mobile Ambients (MA), and as a basis for
query languages on semistructured data. We study some basic questions
concerning the discriminating power of AL, focusing on the equivalence on
processes induced by the logic . As underlying calculi besides MA we
consider a subcalculus in which an image-finiteness condition holds and that we
prove to be Turing complete. Synchronous variants of these calculi are studied
as well. In these calculi, we provide two operational characterisations of
: a coinductive one (as a form of bisimilarity) and an inductive one
(based on structual properties of processes). After showing to be stricly
finer than barbed congruence, we establish axiomatisations of on the
subcalculus of MA (both the asynchronous and the synchronous version), enabling
us to relate to structural congruence. We also present some
(un)decidability results that are related to the above separation properties
for AL: the undecidability of on MA and its decidability on the
subcalculus.Comment: logical methods in computer science, 44 page
On Spatial Conjunction as Second-Order Logic
Spatial conjunction is a powerful construct for reasoning about dynamically
allocated data structures, as well as concurrent, distributed and mobile
computation. While researchers have identified many uses of spatial
conjunction, its precise expressive power compared to traditional logical
constructs was not previously known. In this paper we establish the expressive
power of spatial conjunction. We construct an embedding from first-order logic
with spatial conjunction into second-order logic, and more surprisingly, an
embedding from full second order logic into first-order logic with spatial
conjunction. These embeddings show that the satisfiability of formulas in
first-order logic with spatial conjunction is equivalent to the satisfiability
of formulas in second-order logic. These results explain the great expressive
power of spatial conjunction and can be used to show that adding unrestricted
spatial conjunction to a decidable logic leads to an undecidable logic. As one
example, we show that adding unrestricted spatial conjunction to two-variable
logic leads to undecidability. On the side of decidability, the embedding into
second-order logic immediately implies the decidability of first-order logic
with a form of spatial conjunction over trees. The embedding into spatial
conjunction also has useful consequences: because a restricted form of spatial
conjunction in two-variable logic preserves decidability, we obtain that a
correspondingly restricted form of second-order quantification in two-variable
logic is decidable. The resulting language generalizes the first-order theory
of boolean algebra over sets and is useful in reasoning about the contents of
data structures in object-oriented languages.Comment: 16 page
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
Computational Logic for Biomedicine and Neurosciences
We advocate here the use of computational logic for systems biology, as a
\emph{unified and safe} framework well suited for both modeling the dynamic
behaviour of biological systems, expressing properties of them, and verifying
these properties. The potential candidate logics should have a traditional
proof theoretic pedigree (including either induction, or a sequent calculus
presentation enjoying cut-elimination and focusing), and should come with
certified proof tools. Beyond providing a reliable framework, this allows the
correct encodings of our biological systems. % For systems biology in general
and biomedicine in particular, we have so far, for the modeling part, three
candidate logics: all based on linear logic. The studied properties and their
proofs are formalized in a very expressive (non linear) inductive logic: the
Calculus of Inductive Constructions (CIC). The examples we have considered so
far are relatively simple ones; however, all coming with formal semi-automatic
proofs in the Coq system, which implements CIC. In neuroscience, we are
directly using CIC and Coq, to model neurons and some simple neuronal circuits
and prove some of their dynamic properties. % In biomedicine, the study of
multi omic pathway interactions, together with clinical and electronic health
record data should help in drug discovery and disease diagnosis. Future work
includes using more automatic provers. This should enable us to specify and
study more realistic examples, and in the long term to provide a system for
disease diagnosis and therapy prognosis
Extending Propositional Separation Logic for Robustness Properties
We study an extension of propositional separation logic that can specify robustness properties, such as acyclicity and garbage freedom, for automatic verification of stateful programs with singly-linked lists. We show that its satisfiability problem is PSpace-complete, whereas modest extensions of the logic are shown to be Tower-hard. As separating implication, reachability predicates (under some syntactical restrictions) and a unique quantified variable are allowed, this logic subsumes several PSpace-complete separation logics considered in previous works
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