2,829 research outputs found
Higher-order Linear Logic Programming of Categorial Deduction
We show how categorial deduction can be implemented in higher-order (linear)
logic programming, thereby realising parsing as deduction for the associative
and non-associative Lambek calculi. This provides a method of solution to the
parsing problem of Lambek categorial grammar applicable to a variety of its
extensions.Comment: 8 pages LaTeX, uses eaclap.sty, to appear EACL9
Two Decades of Maude
This paper is a tribute to JosĂ© Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
A Labelled Analytic Theorem Proving Environment for Categorial Grammar
We present a system for the investigation of computational properties of
categorial grammar parsing based on a labelled analytic tableaux theorem
prover. This proof method allows us to take a modular approach, in which the
basic grammar can be kept constant, while a range of categorial calculi can be
captured by assigning different properties to the labelling algebra. The
theorem proving strategy is particularly well suited to the treatment of
categorial grammar, because it allows us to distribute the computational cost
between the algorithm which deals with the grammatical types and the algebraic
checker which constrains the derivation.Comment: 11 pages, LaTeX2e, uses examples.sty and a4wide.st
Nominal C-Unification
Nominal unification is an extension of first-order unification that takes
into account the \alpha-equivalence relation generated by binding operators,
following the nominal approach. We propose a sound and complete procedure for
nominal unification with commutative operators, or nominal C-unification for
short, which has been formalised in Coq. The procedure transforms nominal
C-unification problems into simpler (finite families) of fixpoint problems,
whose solutions can be generated by algebraic techniques on combinatorics of
permutations.Comment: Pre-proceedings paper presented at the 27th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur,
Belgium, 10-12 October 2017 (arXiv:1708.07854
Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining
We investigate unification problems related to the Cipher Block Chaining
(CBC) mode of encryption. We first model chaining in terms of a simple,
convergent, rewrite system over a signature with two disjoint sorts: list and
element. By interpreting a particular symbol of this signature suitably, the
rewrite system can model several practical situations of interest. An inference
procedure is presented for deciding the unification problem modulo this rewrite
system. The procedure is modular in the following sense: any given problem is
handled by a system of `list-inferences', and the set of equations thus derived
between the element-terms of the problem is then handed over to any
(`black-box') procedure which is complete for solving these element-equations.
An example of application of this unification procedure is given, as attack
detection on a Needham-Schroeder like protocol, employing the CBC encryption
mode based on the associative-commutative (AC) operator XOR. The 2-sorted
convergent rewrite system is then extended into one that fully captures a block
chaining encryption-decryption mode at an abstract level, using no AC-symbols;
and unification modulo this extended system is also shown to be decidable.Comment: 26 page
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and NLogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is inspired from
proof theory and more specifically linear logic and Geometry of Interaction.
We show how unification can be used to build a model of computation by means
of specific subalgebras associated to finite permutations groups. We then prove
that whether an observation (the algebraic counterpart of a program) accepts a
word can be decided within logarithmic space. We also show that the
construction can naturally represent pointer machines, an intuitive way of
understanding logarithmic space computing
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
A Lambda Term Representation Inspired by Linear Ordered Logic
We introduce a new nameless representation of lambda terms inspired by
ordered logic. At a lambda abstraction, number and relative position of all
occurrences of the bound variable are stored, and application carries the
additional information where to cut the variable context into function and
argument part. This way, complete information about free variable occurrence is
available at each subterm without requiring a traversal, and environments can
be kept exact such that they only assign values to variables that actually
occur in the associated term. Our approach avoids space leaks in interpreters
that build function closures.
In this article, we prove correctness of the new representation and present
an experimental evaluation of its performance in a proof checker for the
Edinburgh Logical Framework.
Keywords: representation of binders, explicit substitutions, ordered
contexts, space leaks, Logical Framework.Comment: In Proceedings LFMTP 2011, arXiv:1110.668
Towards 3-Dimensional Rewriting Theory
String rewriting systems have proved very useful to study monoids. In good
cases, they give finite presentations of monoids, allowing computations on
those and their manipulation by a computer. Even better, when the presentation
is confluent and terminating, they provide one with a notion of canonical
representative of the elements of the presented monoid. Polygraphs are a
higher-dimensional generalization of this notion of presentation, from the
setting of monoids to the much more general setting of n-categories. One of the
main purposes of this article is to give a progressive introduction to the
notion of higher-dimensional rewriting system provided by polygraphs, and
describe its links with classical rewriting theory, string and term rewriting
systems in particular. After introducing the general setting, we will be
interested in proving local confluence for polygraphs presenting 2-categories
and introduce a framework in which a finite 3-dimensional rewriting system
admits a finite number of critical pairs
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