14,521 research outputs found
Reformulation in planning
Reformulation of a problem is intended to make the problem more amenable to efficient solution. This is equally true in the special case of reformulating a planning problem. This paper considers various ways in which reformulation can be exploited in planning
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets
Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net
model and several translations to networks of timed automata have been proposed
for this model. We present a direct, DBM-based algorithm for forward
reachability analysis of bounded TAPNs extended with transport arcs, inhibitor
arcs and age invariants. We also give a complete proof of its correctness,
including reduction techniques based on symmetries and extrapolation. Finally,
we augment the algorithm with a novel state-space reduction technique
introducing a monotonic ordering on markings and prove its soundness even in
the presence of monotonicity-breaking features like age invariants and
inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and
the experimental results document an encouraging performance compared to
verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587
A dependent nominal type theory
Nominal abstract syntax is an approach to representing names and binding
pioneered by Gabbay and Pitts. So far nominal techniques have mostly been
studied using classical logic or model theory, not type theory. Nominal
extensions to simple, dependent and ML-like polymorphic languages have been
studied, but decidability and normalization results have only been established
for simple nominal type theories. We present a LF-style dependent type theory
extended with name-abstraction types, prove soundness and decidability of
beta-eta-equivalence checking, discuss adequacy and canonical forms via an
example, and discuss extensions such as dependently-typed recursion and
induction principles
Gluing together proof environments: Canonical extensions of LF type theories featuring locks
Ā© F. Honsell, L. Liquori, P. Maksimovic, I. Scagnetto This work is licensed under the Creative Commons Attribution License.We present two extensions of the LF Constructive Type Theory featuring monadic locks. A lock is a monadic type construct that captures the effect of an external call to an oracle. Such calls are the basic tool for gluing together diverse Type Theories and proof development environments. The oracle can be invoked either to check that a constraint holds or to provide a suitable witness. The systems are presented in the canonical style developed by the CMU School. The first system, CLLF/p,is the canonical version of the system LLF p, presented earlier by the authors. The second system, CLLF p?, features the possibility of invoking the oracle to obtain a witness satisfying a given constraint. We discuss encodings of Fitch-Prawitz Set theory, call-by-value Ī»-calculi, and systems of Light Linear Logic. Finally, we show how to use Fitch-Prawitz Set Theory to define a type system that types precisely the strongly normalizing terms
Mechanizing Principia Logico-Metaphysica in Functional Type Theory
Principia Logico-Metaphysica contains a foundational logical theory for
metaphysics, mathematics, and the sciences. It includes a canonical development
of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of
Ernst Mally, formalized by Zalta) that distinguishes between ordinary and
abstract objects.
This article reports on recent work in which AOT has been successfully
represented and partly automated in the proof assistant system Isabelle/HOL.
Initial experiments within this framework reveal a crucial but overlooked fact:
a deeply-rooted and known paradox is reintroduced in AOT when the logic of
complex terms is simply adjoined to AOT's specially-formulated comprehension
principle for relations. This result constitutes a new and important paradox,
given how much expressive and analytic power is contributed by having the two
kinds of complex terms in the system. Its discovery is the highlight of our
joint project and provides strong evidence for a new kind of scientific
practice in philosophy, namely, computational metaphysics.
Our results were made technically possible by a suitable adaptation of
Benzm\"uller's metalogical approach to universal reasoning by semantically
embedding theories in classical higher-order logic. This approach enables one
to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL,
for mechanizing and experimentally exploring challenging logics and theories
such as AOT. Our results also provide a fresh perspective on the question of
whether relational type theory or functional type theory better serves as a
foundation for logic and metaphysics.Comment: 14 pages, 6 figures; preprint of article with same title to appear in
The Review of Symbolic Logi
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