2,027 research outputs found
CCS Dynamic Bisimulation is Progressing
Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g.\ and are woc but and are not. This fact prevents us from characterizing CCS semantics (when is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e.\ run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two characterizations via modal logic in the style of HML, and a complete axiomatization for finite agents. Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents. Thus the title of the paper
Dynamic Congruence vs. Progressing Bisimulation for CCS
Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. \alpha.\tau.\beta.nil and \alpha.\beta.nil are woc but \tau.\beta.nil and \beta.nil are not. This fact prevent us from characterizing CCS semantics (when \tau is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e. run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two logical characterizations via modal logic in the style of HML and a complete axiomatization for finite agents (consisting of the axioms for Strong Observational Congruence and of two of the three Milner's -laws). Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents
Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract
In recent work, Stalnaker proposes a logical framework in which belief is
realized as a weakened form of knowledge. Building on Stalnaker's core
insights, and using frameworks developed by Bjorndahl and Baltag et al., we
employ topological tools to refine and, we argue, improve on this analysis. The
structure of topological subset spaces allows for a natural distinction between
what is known and (roughly speaking) what is knowable; we argue that the
foundational axioms of Stalnaker's system rely intuitively on both of these
notions. More precisely, we argue that the plausibility of the principles
Stalnaker proposes relating knowledge and belief relies on a subtle
equivocation between an "evidence-in-hand" conception of knowledge and a weaker
"evidence-out-there" notion of what could come to be known. Our analysis leads
to a trimodal logic of knowledge, knowability, and belief interpreted in
topological subset spaces in which belief is definable in terms of knowledge
and knowability. We provide a sound and complete axiomatization for this logic
as well as its uni-modal belief fragment. We then consider weaker logics that
preserve suitable translations of Stalnaker's postulates, yet do not allow for
any reduction of belief. We propose novel topological semantics for these
irreducible notions of belief, generalizing our previous semantics, and provide
sound and complete axiomatizations for the corresponding logics.Comment: In Proceedings TARK 2017, arXiv:1707.08250. The full version of this
paper, including the longer proofs, is at arXiv:1612.0205
Vienna Circle and Logical Analysis of Relativity Theory
In this paper we present some of our school's results in the area of building
up relativity theory (RT) as a hierarchy of theories in the sense of logic. We
use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and
we build on experience gained in FOM.
The main aims of our school are the following: We want to base the theory on
simple, unambiguous axioms with clear meanings. It should be absolutely
understandable for any reader what the axioms say and the reader can decide
about each axiom whether he likes it. The theory should be built up from these
axioms in a straightforward, logical manner. We want to provide an analysis of
the logical structure of the theory. We investigate which axioms are needed for
which predictions of RT. We want to make RT more transparent logically, easier
to understand, easier to change, modular, and easier to teach. We want to
obtain deeper understanding of RT.
Our work can be considered as a case-study showing that the Vienna Circle's
(VC) approach to doing science is workable and fruitful when performed with
using the insights and tools of mathematical logic acquired since its formation
years at the very time of the VC activity. We think that logical positivism was
based on the insight and anticipation of what mathematical logic is capable
when elaborated to some depth. Logical positivism, in great part represented by
VC, influenced and took part in the birth of modern mathematical logic. The
members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure
Axiomatizing Flat Iteration
Flat iteration is a variation on the original binary version of the Kleene
star operation P*Q, obtained by restricting the first argument to be a sum of
atomic actions. It generalizes prefix iteration, in which the first argument is
a single action. Complete finite equational axiomatizations are given for five
notions of bisimulation congruence over basic CCS with flat iteration, viz.
strong congruence, branching congruence, eta-congruence, delay congruence and
weak congruence. Such axiomatizations were already known for prefix iteration
and are known not to exist for general iteration. The use of flat iteration has
two main advantages over prefix iteration: 1.The current axiomatizations
generalize to full CCS, whereas the prefix iteration approach does not allow an
elimination theorem for an asynchronous parallel composition operator. 2.The
greater expressiveness of flat iteration allows for much shorter completeness
proofs.
In the setting of prefix iteration, the most convenient way to obtain the
completeness theorems for eta-, delay, and weak congruence was by reduction to
the completeness theorem for branching congruence. In the case of weak
congruence this turned out to be much simpler than the only direct proof found.
In the setting of flat iteration on the other hand, the completeness theorems
for delay and weak (but not eta-) congruence can equally well be obtained by
reduction to the one for strong congruence, without using branching congruence
as an intermediate step. Moreover, the completeness results for prefix
iteration can be retrieved from those for flat iteration, thus obtaining a
second indirect approach for proving completeness for delay and weak congruence
in the setting of prefix iteration.Comment: 15 pages. LaTeX 2.09. Filename: flat.tex.gz. On A4 paper print with:
dvips -t a4 -O -2.15cm,-2.22cm -x 1225 flat. For US letter with: dvips -t
letter -O -0.73in,-1.27in -x 1225 flat. More info at
http://theory.stanford.edu/~rvg/abstracts.html#3
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