465 research outputs found
Indexed linear logic and higher-order model checking
In recent work, Kobayashi observed that the acceptance by an alternating tree
automaton A of an infinite tree T generated by a higher-order recursion scheme
G may be formulated as the typability of the recursion scheme G in an
appropriate intersection type system associated to the automaton A. The purpose
of this article is to establish a clean connection between this line of work
and Bucciarelli and Ehrhard's indexed linear logic. This is achieved in two
steps. First, we recast Kobayashi's result in an equivalent infinitary
intersection type system where intersection is not idempotent anymore. Then, we
show that the resulting type system is a fragment of an infinitary version of
Bucciarelli and Ehrhard's indexed linear logic. While this work is very
preliminary and does not integrate key ingredients of higher-order
model-checking like priorities, it reveals an interesting and promising
connection between higher-order model-checking and linear logic.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
Relational type-checking for MELL proof-structures. Part 1: Multiplicatives
Relational semantics for linear logic is a form of non-idempotent
intersection type system, from which several informations on the execution of a
proof-structure can be recovered. An element of the relational interpretation
of a proof-structure R with conclusion acts thus as a type (refining
) having R as an inhabitant. We are interested in the following
type-checking question: given a proof-structure R, a list of formulae ,
and a point x in the relational interpretation of , is x in the
interpretation of R? This question is decidable. We present here an algorithm
that decides it in time linear in the size of R, if R is a proof-structure in
the multiplicative fragment of linear logic. This algorithm can be extended to
larger fragments of multiplicative-exponential linear logic containing
-calculus
Relational semantics of linear logic and higher-order model-checking
In this article, we develop a new and somewhat unexpected connection between
higher-order model-checking and linear logic. Our starting point is the
observation that once embedded in the relational semantics of linear logic, the
Church encoding of any higher-order recursion scheme (HORS) comes together with
a dual Church encoding of an alternating tree automata (ATA) of the same
signature. Moreover, the interaction between the relational interpretations of
the HORS and of the ATA identifies the set of accepting states of the tree
automaton against the infinite tree generated by the recursion scheme. We show
how to extend this result to alternating parity automata (APT) by introducing a
parametric version of the exponential modality of linear logic, capturing the
formal properties of colors (or priorities) in higher-order model-checking. We
show in particular how to reunderstand in this way the type-theoretic approach
to higher-order model-checking developed by Kobayashi and Ong. We briefly
explain in the end of the paper how his analysis driven by linear logic results
in a new and purely semantic proof of decidability of the formulas of the
monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte
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