3,618 research outputs found
On the Complexity of Existential Positive Queries
We systematically investigate the complexity of model checking the
existential positive fragment of first-order logic. In particular, for a set of
existential positive sentences, we consider model checking where the sentence
is restricted to fall into the set; a natural question is then to classify
which sentence sets are tractable and which are intractable. With respect to
fixed-parameter tractability, we give a general theorem that reduces this
classification question to the corresponding question for primitive positive
logic, for a variety of representations of structures. This general theorem
allows us to deduce that an existential positive sentence set having bounded
arity is fixed-parameter tractable if and only if each sentence is equivalent
to one in bounded-variable logic. We then use the lens of classical complexity
to study these fixed-parameter tractable sentence sets. We show that such a set
can be NP-complete, and consider the length needed by a translation from
sentences in such a set to bounded-variable logic; we prove superpolynomial
lower bounds on this length using the theory of compilability, obtaining an
interesting type of formula size lower bound. Overall, the tools, concepts, and
results of this article set the stage for the future consideration of the
complexity of model checking on more expressive logics
The Complexity of Model Checking (Collapsible) Higher-Order Pushdown Systems
We study (collapsible) higher-order pushdown systems --- theoretically robust and well-studied models of higher-order programs --- along with their natural subclass called (collapsible) higher-order basic process algebras. We provide a comprehensive analysis of the model checking complexity of a range of both branching-time and linear-time temporal logics. We obtain tight bounds on data, expression, and combined-complexity for both (collapsible) higher-order pushdown systems and (collapsible) higher-order basic process algebra. At order-, results range from polynomial to -exponential time. Finally, we study (collapsible) higher-order basic process algebras as graph generators and show that they are almost as powerful as (collapsible) higher-order pushdown systems up to MSO interpretations
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
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