47,035 research outputs found
Weighted Logics for Nested Words and Algebraic Formal Power Series
Nested words, a model for recursive programs proposed by Alur and Madhusudan,
have recently gained much interest. In this paper we introduce quantitative
extensions and study nested word series which assign to nested words elements
of a semiring. We show that regular nested word series coincide with series
definable in weighted logics as introduced by Droste and Gastin. For this we
establish a connection between nested words and the free bisemigroup. Applying
our result, we obtain characterizations of algebraic formal power series in
terms of weighted logics. This generalizes results of Lautemann, Schwentick and
Therien on context-free languages
Decidable Exponentials in Nonassociative Noncommutative Linear Logic
The use of exponentials in linear logic greatly enhances its expressive
power. In this paper we focus on nonassociative noncommutative multiplicative
linear logic, and systematically explore modal axioms K, T, and 4 as well as
the structural rules of contraction and weakening. We give sequent systems for
each subset of these axioms; these enjoy cut elimination and have analogues in
more structural logics. We then appeal to work of Bulinska extending work of
Buszkowski to show that several of these logics are PTIME decidable and
generate context free languages as categorial grammars. This contrasts
associative systems where similar logics are known to generate all recursively
enumerable languages, and are thus in particular undecidable
Extended Computation Tree Logic
We introduce a generic extension of the popular branching-time logic CTL
which refines the temporal until and release operators with formal languages.
For instance, a language may determine the moments along a path that an until
property may be fulfilled. We consider several classes of languages leading to
logics with different expressive power and complexity, whose importance is
motivated by their use in model checking, synthesis, abstract interpretation,
etc.
We show that even with context-free languages on the until operator the logic
still allows for polynomial time model-checking despite the significant
increase in expressive power. This makes the logic a promising candidate for
applications in verification.
In addition, we analyse the complexity of satisfiability and compare the
expressive power of these logics to CTL* and extensions of PDL
Non-Rigid Designators in Epistemic and Temporal Free Description Logics (Extended Version)
Definite descriptions, such as 'the smallest planet in the Solar System',
have been recently recognised as semantically transparent devices for object
identification in knowledge representation formalisms. Along with individual
names, they have been introduced also in the context of description logic
languages, enriching the expressivity of standard nominal constructors.
Moreover, in the first-order modal logic literature, definite descriptions have
been widely investigated for their non-rigid behaviour, which allows them to
denote different objects at different states. In this direction, we introduce
epistemic and temporal extensions of standard description logics, with nominals
and the universal role, additionally equipped with definite descriptions
constructors. Regarding names and descriptions, in these languages we allow
for: possible lack of denotation, ensured by partial models, coming from free
logic semantics as a generalisation of the classical ones; and non-rigid
designation features, obtained by assigning to terms distinct values across
states, as opposed to the standard rigidity condition on individual
expressions. In the absence of the rigid designator assumption, we show that
the satisfiability problem for epistemic free description logics is
NExpTime-complete, while satisfiability for temporal free description logics
over linear time structures is undecidable
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
On Second-Order Monadic Monoidal and Groupoidal Quantifiers
We study logics defined in terms of second-order monadic monoidal and
groupoidal quantifiers. These are generalized quantifiers defined by monoid and
groupoid word-problems, equivalently, by regular and context-free languages. We
give a computational classification of the expressive power of these logics
over strings with varying built-in predicates. In particular, we show that
ATIME(n) can be logically characterized in terms of second-order monadic
monoidal quantifiers
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Wreath Products of Forest Algebras, with Applications to Tree Logics
We use the recently developed theory of forest algebras to find algebraic
characterizations of the languages of unranked trees and forests definable in
various logics. These include the temporal logics CTL and EF, and first-order
logic over the ancestor relation. While the characterizations are in general
non-effective, we are able to use them to formulate necessary conditions for
definability and provide new proofs that a number of languages are not
definable in these logics
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