191 research outputs found
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
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
Layered logics, coalgebraically
This short note revisits layered logics from a coalgebraic point of view, and proposes a
naturality condition to express the typical hierarchical requirement under which all abstract transitions
should be traceable in more specialised layers.NORTE-01-0145-FEDER-000037. ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation through (a) COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, project POCI-01-0145-FEDER-016826, and (b) Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, within project NORTE-01-0145-FEDER-00003
Coalgebra for the working software engineer
Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to spec ify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified.Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems
The Alternating-Time \mu-Calculus With Disjunctive Explicit Strategies
Alternating-time temporal logic (ATL) and its extensions, including the
alternating-time -calculus (AMC), serve the specification of the strategic
abilities of coalitions of agents in concurrent game structures. The key
ingredient of the logic are path quantifiers specifying that some coalition of
agents has a joint strategy to enforce a given goal. This basic setup has been
extended to let some of the agents (revocably) commit to using certain named
strategies, as in ATL with explicit strategies (ATLES). In the present work, we
extend ATLES with fixpoint operators and strategy disjunction, arriving at the
alternating-time -calculus with disjunctive explicit strategies (AMCDES),
which allows for a more flexible formulation of temporal properties (e.g.
fairness) and, through strategy disjunction, a form of controlled
nondeterminism in commitments. Our main result is an ExpTime upper bound for
satisfiability checking (which is thus ExpTime-complete). We also prove upper
bounds QP (quasipolynomial time) and NP coNP for model checking under
fixed interpretations of explicit strategies, and NP under open interpretation.
Our key technical tool is a treatment of the AMCDES within the generic
framework of coalgebraic logic, which in particular reduces the analysis of
most reasoning tasks to the treatment of a very simple one-step logic featuring
only propositional operators and next-step operators without nesting; we give a
new model construction principle for this one-step logic that relies on a
set-valued variant of first-order resolution.Comment: Full version with appendix as well as corrected set-valued resolution
metho
A method for rigorous design of reconfigurable systems
Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements.
In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.This work is financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation – COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The first author is further supported by the BPD FCT Grant SFRH/BPD/103004/2014, and R. Neves is sponsored by FCT Grant SFRH/BD/52234/2013. M.A. Martins is also funded by the EU FP7 Marie Curie PIRSESGA-2012-318986 project GeTFun: Generalizing Truth-Functionality
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