2,197 research outputs found
A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems
We address a fundamental mismatch between the combinations of dynamics that
occur in cyber-physical systems and the limited kinds of dynamics supported in
analysis. Modern applications combine communication, computation, and control.
They may even form dynamic distributed networks, where neither structure nor
dimension stay the same while the system follows hybrid dynamics, i.e., mixed
discrete and continuous dynamics. We provide the logical foundations for
closing this analytic gap. We develop a formal model for distributed hybrid
systems. It combines quantified differential equations with quantified
assignments and dynamic dimensionality-changes. We introduce a dynamic logic
for verifying distributed hybrid systems and present a proof calculus for this
logic. This is the first formal verification approach for distributed hybrid
systems. We prove that our calculus is a sound and complete axiomatization of
the behavior of distributed hybrid systems relative to quantified differential
equations. In our calculus we have proven collision freedom in distributed car
control even when an unbounded number of new cars may appear dynamically on the
road
The Doxastic Interpretation of Team Semantics
We advance a doxastic interpretation for many of the logical connectives
considered in Dependence Logic and in its extensions, and we argue that Team
Semantics is a natural framework for reasoning about beliefs and belief
updates
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
Binding bound variables in epistemic contexts
ABSTRACT Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's ‘objectual’ interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields the undesirable result that any attempt to ‘quantify in’ to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality
A Uniform Substitution Calculus for Differential Dynamic Logic
This paper introduces a new proof calculus for differential dynamic logic
(dL) that is entirely based on uniform substitution, a proof rule that
substitutes a formula for a predicate symbol everywhere. Uniform substitutions
make it possible to rely on axioms rather than axiom schemata, substantially
simplifying implementations. Instead of nontrivial schema variables and
soundness-critical side conditions on the occurrence patterns of variables, the
resulting calculus adopts only a finite number of ordinary dL formulas as
axioms. The static semantics of differential dynamic logic is captured
exclusively in uniform substitutions and bound variable renamings as opposed to
being spread in delicate ways across the prover implementation. In addition to
sound uniform substitutions, this paper introduces differential forms for
differential dynamic logic that make it possible to internalize differential
invariants, differential substitutions, and derivations as first-class axioms
in dL
Specificity distinction
This paper is concerned with semantic noun phrase typology, focusing on the question of how to draw fine-grained distinctions necessary for an accurate account of natural language phenomena. In the extensive literature on this topic, the most commonly encountered parameters of classification concern the semantic type of the denotation of the noun phrase, the familiarity or novelty of its referent, the quantificational/nonquantificational distinction (connected to the weak/strong dichotomy), as well as, more recently, the question of whether the noun phrase is choice-functional or not (see Reinhart 1997, Winter 1997, Kratzer 1998, Matthewson 1999). In the discussion that follows I will attempt to make the following general points: (i) phenomena involving the behavior of noun phrases both within and across languages point to the need of establishing further distinctions that are too fine-grained to be caught in the net of these typologies; (ii) some of the relevant distinctions can be captured in terms of conditions on assignment functions; (iii) distribution and scopal peculiarities of noun phrases may result from constraints they impose on the way variables they introduce are to be assigned values.
Section 2 reviews the typology of definite noun phrases introduced in Farkas 2000 and the way it provides support for the general points above. Section 3 examines some of the problems raised by recognizing the rich variety of 'indefinite' noun phrases found in natural language and by attempting to capture their distribution and interpretation. Common to the typologies discussed in the two sections is the issue of marking different types of variation in the interpretation of a noun phrase. In the light of this discussion, specificity turns out to be an epiphenomenon connected to a family of distinctions that are marked differently in different languages
De Re Updates
In this paper, we propose a lightweight yet powerful dynamic epistemic logic
that captures not only the distinction between de dicto and de re knowledge but
also the distinction between de dicto and de re updates. The logic is based on
the dynamified version of an epistemic language extended with the assignment
operator borrowed from dynamic logic, following the work of Wang and Seligman
(Proc. AiML 2018). We obtain complete axiomatizations for the counterparts of
public announcement logic and event-model-based DEL based on new reduction
axioms taking care of the interactions between dynamics and assignments.Comment: In Proceedings TARK 2021, arXiv:2106.1088
Ontology of sentential moods
In this paper ontological implications of the Barcan formula and its converse will be discussed at the conceptual and technical level. The thesis that will be defended is that sentential moods are not ontologically neutral since the rejection of ontological implications of Barcan formula and its converse is a condition of a possibility of the imperative mood. The paper is divided into four sections. In the first section a systematization of semantical systems of quantified modal logic is introduced for the purpose of making explicit their ontological presuppositions. In this context Jadacki's ontological difference between being and existence is discussed and analyzed within the framework of hereby proposed system of quantified modal logic. The second section discusses ontological implications of the Barcan formula and its converse within the system accommodating the difference between being and existence. The third section presents a proof of incompatibility of the Barcan formula and its converse with the use of imperatives. In the concluding section, a thesis on logical pragmatics foreclosing the dilemma between necessitism and contingentism is put forward and defended against some objections
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