486 research outputs found
Automating Access Control Logics in Simple Type Theory with LEO-II
Garg and Abadi recently proved that prominent access control logics can be
translated in a sound and complete way into modal logic S4. We have previously
outlined how normal multimodal logics, including monomodal logics K and S4, can
be embedded in simple type theory (which is also known as higher-order logic)
and we have demonstrated that the higher-order theorem prover LEO-II can
automate reasoning in and about them. In this paper we combine these results
and describe a sound and complete embedding of different access control logics
in simple type theory. Employing this framework we show that the off the shelf
theorem prover LEO-II can be applied to automate reasoning in prominent access
control logics.Comment: ii + 20 page
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
The Higher-Order Prover Leo-II.
Leo-II is an automated theorem prover for classical higher-order logic. The prover has pioneered cooperative higher-order-first-order proof automation, it has influenced the development of the TPTP THF infrastructure for higher-order logic, and it has been applied in a wide array of problems. Leo-II may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants. Recent progress in this direction is reported for the Isabelle/HOL system.The Leo-II project has been supported by the following grants: EPSRC grant EP/D070511/1 and DFG grants BE/2501 6-1, 8-1 and 9-1.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10817-015-9348-y
Extensional Higher-Order Paramodulation in Leo-III
Leo-III is an automated theorem prover for extensional type theory with
Henkin semantics and choice. Reasoning with primitive equality is enabled by
adapting paramodulation-based proof search to higher-order logic. The prover
may cooperate with multiple external specialist reasoning systems such as
first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP
framework for input formats, reporting results and proofs, and standardized
communication between reasoning systems, enabling e.g. proof reconstruction
from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning
in polymorphic first-order and higher-order logic, in all normal quantified
modal logics, as well as in different deontic logics. Its development had
initiated the ongoing extension of the TPTP infrastructure to reasoning within
non-classical logics.Comment: 34 pages, 7 Figures, 1 Table; submitted articl
Recent Successes with a Meta-Logical Approach to Universal Logical Reasoning (Extended Abstract)
The quest for a most general framework supporting universal reasoning is very prominently represented in the works of Leibniz. He envisioned a scientia generalis founded on a characteristica universalis, that is, a most universal formal language in which all knowledge about the world and the sciences can be encoded. A quick study of the survey literature on logical formalisms suggests that quite the opposite to Leibniz’ dream has become reality. Instead of a characteristica universalis, we are today facing a very rich and heterogenous zoo of different logical systems, and instead of converging towards a single superior logic, this logic zoo is further expanding, eventually even at accelerated pace. As a consequence, the unified vision of Leibniz seems farther away than ever before. However, there are also some promising initiatives to counteract these diverging developments. Attempts at unifying approaches to logic include categorial logic algebraic logic and coalgebraic logic
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