22,841 research outputs found
Finding Finite Models in Multi-Sorted First-Order Logic
This work extends the existing MACE-style finite model finding approach to
multi-sorted first order logic. This existing approach iteratively assumes
increasing domain sizes and encodes the related ground problem as a SAT
problem. When moving to the multi-sorted setting each sort may have a different
domain size, leading to an explosion in the search space. This paper focusses
on methods to tame that search space. The key approach adds additional
information to the SAT encoding to suggest which domains should be grown.
Evaluation of an implementation of techniques in the Vampire theorem prover
shows that they dramatically reduce the search space and that this is an
effective approach to find finite models in multi-sorted first order logic.Comment: SAT 201
Inquisitive bisimulation
Inquisitive modal logic InqML is a generalisation of standard Kripke-style
modal logic. In its epistemic incarnation, it extends standard epistemic logic
to capture not just the information that agents have, but also the questions
that they are interested in. Technically, InqML fits within the family of
logics based on team semantics. From a model-theoretic perspective, it takes us
a step in the direction of monadic second-order logic, as inquisitive modal
operators involve quantification over sets of worlds. We introduce and
investigate the natural notion of bisimulation equivalence in the setting of
InqML. We compare the expressiveness of InqML and first-order logic in the
context of relational structures with two sorts, one for worlds and one for
information states. We characterise inquisitive modal logic, as well as its
multi-agent epistemic S5-like variant, as the bisimulation invariant fragment
of first-order logic over various natural classes of two-sorted structures.
These results crucially require non-classical methods in studying bisimulation
and first-order expressiveness over non-elementary classes of structures,
irrespective of whether we aim for characterisations in the sense of classical
or of finite model theory
Bisimulation in Inquisitive Modal Logic
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style
modal logic. In its epistemic incarnation, it extends standard epistemic logic
to capture not just the information that agents have, but also the questions
that they are interested in. Technically, InqML fits within the family of
logics based on team semantics. From a model-theoretic perspective, it takes us
a step in the direction of monadic second-order logic, as inquisitive modal
operators involve quantification over sets of worlds. We introduce and
investigate the natural notion of bisimulation equivalence in the setting of
InqML. We compare the expressiveness of InqML and first-order logic, and
characterise inquisitive modal logic as the bisimulation invariant fragments of
first-order logic over various classes of two-sorted relational structures.
These results crucially require non-classical methods in studying bisimulations
and first-order expressiveness over non-elementary classes.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Adaptability Checking in Multi-Level Complex Systems
A hierarchical model for multi-level adaptive systems is built on two basic
levels: a lower behavioural level B accounting for the actual behaviour of the
system and an upper structural level S describing the adaptation dynamics of
the system. The behavioural level is modelled as a state machine and the
structural level as a higher-order system whose states have associated logical
formulas (constraints) over observables of the behavioural level. S is used to
capture the global and stable features of B, by a defining set of allowed
behaviours. The adaptation semantics is such that the upper S level imposes
constraints on the lower B level, which has to adapt whenever it no longer can
satisfy them. In this context, we introduce weak and strong adaptabil- ity,
i.e. the ability of a system to adapt for some evolution paths or for all
possible evolutions, respectively. We provide a relational characterisation for
these two notions and we show that adaptability checking, i.e. deciding if a
system is weak or strong adaptable, can be reduced to a CTL model checking
problem. We apply the model and the theoretical results to the case study of
motion control of autonomous transport vehicles.Comment: 57 page, 10 figures, research papaer, submitte
- …