702 research outputs found
Modal logics are coalgebraic
Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility
Approximate reasoning for real-time probabilistic processes
We develop a pseudo-metric analogue of bisimulation for generalized
semi-Markov processes. The kernel of this pseudo-metric corresponds to
bisimulation; thus we have extended bisimulation for continuous-time
probabilistic processes to a much broader class of distributions than
exponential distributions. This pseudo-metric gives a useful handle on
approximate reasoning in the presence of numerical information -- such as
probabilities and time -- in the model. We give a fixed point characterization
of the pseudo-metric. This makes available coinductive reasoning principles for
reasoning about distances. We demonstrate that our approach is insensitive to
potentially ad hoc articulations of distance by showing that it is intrinsic to
an underlying uniformity. We provide a logical characterization of this
uniformity using a real-valued modal logic. We show that several quantitative
properties of interest are continuous with respect to the pseudo-metric. Thus,
if two processes are metrically close, then observable quantitative properties
of interest are indeed close.Comment: Preliminary version appeared in QEST 0
Disjunctive bases: normal forms and model theory for modal logics
We present the concept of a disjunctive basis as a generic framework for
normal forms in modal logic based on coalgebra. Disjunctive bases were defined
in previous work on completeness for modal fixpoint logics, where they played a
central role in the proof of a generic completeness theorem for coalgebraic
mu-calculi. Believing the concept has a much wider significance, here we
investigate it more thoroughly in its own right. We show that the presence of a
disjunctive basis at the "one-step" level entails a number of good properties
for a coalgebraic mu-calculus, in particular, a simulation theorem showing that
every alternating automaton can be transformed into an equivalent
nondeterministic one. Based on this, we prove a Lyndon theorem for the full
fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform
Interpolation result, for both the full mu-calculus and its fixpoint-free
fragment, and a Janin-Walukiewicz-style characterization theorem for the
mu-calculus under slightly stronger assumptions.
We also raise the questions, when a disjunctive basis exists, and how
disjunctive bases are related to Moss' coalgebraic "nabla" modalities. Nabla
formulas provide disjunctive bases for many coalgebraic modal logics, but there
are cases where disjunctive bases give useful normal forms even when nabla
formulas fail to do so, our prime example being graded modal logic. We also
show that disjunctive bases are preserved by forming sums, products and
compositions of coalgebraic modal logics, providing tools for modular
construction of modal logics admitting disjunctive bases. Finally, we consider
the problem of giving a category-theoretic formulation of disjunctive bases,
and provide a partial solution
Finite-state Strategies in Delay Games (full version)
What is a finite-state strategy in a delay game? We answer this surprisingly
non-trivial question by presenting a very general framework that allows to
remove delay: finite-state strategies exist for all winning conditions where
the resulting delay-free game admits a finite-state strategy. The framework is
applicable to games whose winning condition is recognized by an automaton with
an acceptance condition that satisfies a certain aggregation property. Our
framework also yields upper bounds on the complexity of determining the winner
of such delay games and upper bounds on the necessary lookahead to win the
game. In particular, we cover all previous results of that kind as special
cases of our uniform approach
Factory of realities: on the emergence of virtual spatiotemporal structures
The ubiquitous nature of modern Information Retrieval and Virtual World give
rise to new realities. To what extent are these "realities" real? Which
"physics" should be applied to quantitatively describe them? In this essay I
dwell on few examples. The first is Adaptive neural networks, which are not
networks and not neural, but still provide service similar to classical ANNs in
extended fashion. The second is the emergence of objects looking like
Einsteinian spacetime, which describe the behavior of an Internet surfer like
geodesic motion. The third is the demonstration of nonclassical and even
stronger-than-quantum probabilities in Information Retrieval, their use.
Immense operable datasets provide new operationalistic environments, which
become to greater and greater extent "realities". In this essay, I consider the
overall Information Retrieval process as an objective physical process,
representing it according to Melucci metaphor in terms of physical-like
experiments. Various semantic environments are treated as analogs of various
realities. The readers' attention is drawn to topos approach to physical
theories, which provides a natural conceptual and technical framework to cope
with the new emerging realities.Comment: 21 p
Near-Optimal Scheduling for LTL with Future Discounting
We study the search problem for optimal schedulers for the linear temporal
logic (LTL) with future discounting. The logic, introduced by Almagor, Boker
and Kupferman, is a quantitative variant of LTL in which an event in the far
future has only discounted contribution to a truth value (that is a real number
in the unit interval [0, 1]). The precise problem we study---it naturally
arises e.g. in search for a scheduler that recovers from an internal error
state as soon as possible---is the following: given a Kripke frame, a formula
and a number in [0, 1] called a margin, find a path of the Kripke frame that is
optimal with respect to the formula up to the prescribed margin (a truly
optimal path may not exist). We present an algorithm for the problem; it works
even in the extended setting with propositional quality operators, a setting
where (threshold) model-checking is known to be undecidable
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