690,703 research outputs found
Indicative Conditionals and Dynamic Epistemic Logic
Recent ideas about epistemic modals and indicative conditionals in formal
semantics have significant overlap with ideas in modal logic and dynamic
epistemic logic. The purpose of this paper is to show how greater interaction
between formal semantics and dynamic epistemic logic in this area can be of
mutual benefit. In one direction, we show how concepts and tools from modal
logic and dynamic epistemic logic can be used to give a simple, complete
axiomatization of Yalcin's [16] semantic consequence relation for a language
with epistemic modals and indicative conditionals. In the other direction, the
formal semantics for indicative conditionals due to Kolodny and MacFarlane [9]
gives rise to a new dynamic operator that is very natural from the point of
view of dynamic epistemic logic, allowing succinct expression of dependence (as
in dependence logic) or supervenience statements. We prove decidability for the
logic with epistemic modals and Kolodny and MacFarlane's indicative conditional
via a full and faithful computable translation from their logic to the modal
logic K45.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Parametric Linear Dynamic Logic
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear
Dynamic Logic (LDL) by temporal operators equipped with parameters that bound
their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL)
that is able to express all -regular specifications while still
maintaining many of LTL's desirable properties like an intuitive syntax and a
translation into non-deterministic B\"uchi automata of exponential size. But
LDL lacks capabilities to express timing constraints. By adding parameterized
operators to LDL, we obtain a logic that is able to express all
-regular properties and that subsumes parameterized extensions of LTL
like Parametric LTL and PROMPT-LTL. Our main technical contribution is a
translation of PLDL formulas into non-deterministic B\"uchi word automata of
exponential size via alternating automata. This yields a PSPACE model checking
algorithm and a realizability algorithm with doubly-exponential running time.
Furthermore, we give tight upper and lower bounds on optimal parameter values
for both problems. These results show that PLDL model checking and
realizability are not harder than LTL model checking and realizability.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Transition Semantics - The Dynamics of Dependence Logic
We examine the relationship between Dependence Logic and game logics. A
variant of Dynamic Game Logic, called Transition Logic, is developed, and we
show that its relationship with Dependence Logic is comparable to the one
between First-Order Logic and Dynamic Game Logic discussed by van Benthem. This
suggests a new perspective on the interpretation of Dependence Logic formulas,
in terms of assertions about reachability in games of im- perfect information
against Nature. We then capitalize on this intuition by developing expressively
equivalent variants of Dependence Logic in which this interpretation is taken
to the foreground
Dynamic Logic of Common Knowledge in a Proof Assistant
Common Knowledge Logic is meant to describe situations of the real world
where a group of agents is involved. These agents share knowledge and make
strong statements on the knowledge of the other agents (the so called
\emph{common knowledge}). But as we know, the real world changes and overall
information on what is known about the world changes as well. The changes are
described by dynamic logic. To describe knowledge changes, dynamic logic should
be combined with logic of common knowledge. In this paper we describe
experiments which we have made about the integration in a unique framework of
common knowledge logic and dynamic logic in the proof assistant \Coq. This
results in a set of fully checked proofs for readable statements. We describe
the framework and how a proof can beComment: 15
Language Idling and Language in Use Wittgenstein on Following Rules
This paper has a simple goal: it aims to present
the difference between static logic and dynamic grammar.
At the same time I will stress another difference which
traverses logic and grammar: the difference between
language idling and language in use. There is a
development from static logic to dynamic grammar in
Wittgenstein"s philosophy from early to late, whereas the
difference between language idling and language in use
pervades the whole oeuvre. Therefore I shall distinguish
between four different conditions pertaining to the attempt
to render the relations that hold language together. We find
in early Wittgenstein "idle static logic" and "static logic in
use," and in late Wittgenstein "idle dynamic grammar" and
"dynamic grammar in use." This four-fold distinction serves
to emphasize that the crucial shift to "use," which is usually
claimed to be a feature of the Philosophical Investigations,
already takes place in the Tractatus. A negligence of this
"double shift" from logic to grammar and from idle language
to language in use brought about a vast amount of
misapprehensions of Wittgenstein"s philosophy, especially
of the account of rule following
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