2,219 research outputs found
The Glory of the Past and Geometrical Concurrency
This paper contributes to the general understanding of the geometrical model
of concurrency that was named higher dimensional automata (HDAs) by Pratt. In
particular we investigate modal logics for such models and their expressive
power in terms of the bisimulation that can be captured. The geometric model of
concurrency is interesting from two main reasons: its generality and
expressiveness, and the natural way in which autoconcurrency and action
refinement are captured. Logics for this model, though, are not well
investigated, where a simple, yet adequate, modal logic over HDAs was only
recently introduced. As this modal logic, with two existential modalities,
during and after, captures only split bisimulation, which is rather low in the
spectrum of van Glabbeek and Vaandrager, the immediate question was what small
extension of this logic could capture the more fine-grained hereditary history
preserving bisimulation (hh)? In response, the work in this paper provides
several insights. One is the fact that the geometrical aspect of HDAs makes it
possible to use for capturing the hh-bisimulation, a standard modal logic that
does not employ event variables, opposed to the two logics (over less
expressive models) that we compare with. The logic that we investigate here
uses standard past modalities and extends the previously introduced logic
(called HDML) that had only forward, action-labelled, modalities. Besides, we
try to understand better the above issues by introducing a related model that
we call ST-configuration structures, which extend the configuration structures
of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and
prove the earlier results in the light of this new model. These offer a
different view on why the past modalities and geometrical concurrency capture
the hereditary history preserving bisimulation. Additional correlating insights
are also gained.Comment: 17 pages, 7 figure
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
A New General Method to Generate Random Modal Formulae for Testing Decision Procedures
The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF_[]m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests
A New General Method to Generate Random Modal Formulae for Testing Decision Procedures
The recent emergence of heavily-optimized modal decision procedures has
highlighted the key role of empirical testing in this domain. Unfortunately,
the introduction of extensive empirical tests for modal logics is recent, and
so far none of the proposed test generators is very satisfactory. To cope with
this fact, we present a new random generation method that provides benefits
over previous methods for generating empirical tests. It fixes and much
generalizes one of the best-known methods, the random CNF_[]m test, allowing
for generating a much wider variety of problems, covering in principle the
whole input space. Our new method produces much more suitable test sets for the
current generation of modal decision procedures. We analyze the features of the
new method by means of an extensive collection of empirical tests
Questions and Answers about Oppositions
A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations.
In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis.
A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth
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