45,772 research outputs found
States and exceptions considered as dual effects
In this paper we consider the two major computational effects of states and
exceptions, from the point of view of diagrammatic logics. We get a surprising
result: there exists a symmetry between these two effects, based on the
well-known categorical duality between products and coproducts. More precisely,
the lookup and update operations for states are respectively dual to the throw
and catch operations for exceptions. This symmetry is deeply hidden in the
programming languages; in order to unveil it, we start from the monoidal
equational logic and we add progressively the logical features which are
necessary for dealing with either effect. This approach gives rise to a new
point of view on states and exceptions, which bypasses the problems due to the
non-algebraicity of handling exceptions
Adjunctions for exceptions
An algebraic method is used to study the semantics of exceptions in computer
languages. The exceptions form a computational effect, in the sense that there
is an apparent mismatch between the syntax of exceptions and their intended
semantics. We solve this apparent contradiction by efining a logic for
exceptions with a proof system which is close to their syntax and where their
intended semantics can be seen as a model. This requires a robust framework for
logics and their morphisms, which is provided by categorical tools relying on
adjunctions, fractions and limit sketches.Comment: In this Version 2, minor improvements are made to Version
Named Models in Coalgebraic Hybrid Logic
Hybrid logic extends modal logic with support for reasoning about individual
states, designated by so-called nominals. We study hybrid logic in the broad
context of coalgebraic semantics, where Kripke frames are replaced with
coalgebras for a given functor, thus covering a wide range of reasoning
principles including, e.g., probabilistic, graded, default, or coalitional
operators. Specifically, we establish generic criteria for a given coalgebraic
hybrid logic to admit named canonical models, with ensuing completeness proofs
for pure extensions on the one hand, and for an extended hybrid language with
local binding on the other. We instantiate our framework with a number of
examples. Notably, we prove completeness of graded hybrid logic with local
binding
A New Game Equivalence and its Modal Logic
We revisit the crucial issue of natural game equivalences, and semantics of
game logics based on these. We present reasons for investigating finer concepts
of game equivalence than equality of standard powers, though staying short of
modal bisimulation. Concretely, we propose a more finegrained notion of
equality of "basic powers" which record what players can force plus what they
leave to others to do, a crucial feature of interaction. This notion is closer
to game-theoretic strategic form, as we explain in detail, while remaining
amenable to logical analysis. We determine the properties of basic powers via a
new representation theorem, find a matching "instantial neighborhood game
logic", and show how our analysis can be extended to a new game algebra and
dynamic game logic.Comment: In Proceedings TARK 2017, arXiv:1707.0825
- …