37 research outputs found
Clausal Resolution for Modal Logics of Confluence
We present a clausal resolution-based method for normal multimodal logics of
confluence, whose Kripke semantics are based on frames characterised by
appropriate instances of the Church-Rosser property. Here we restrict attention
to eight families of such logics. We show how the inference rules related to
the normal logics of confluence can be systematically obtained from the
parametrised axioms that characterise such systems. We discuss soundness,
completeness, and termination of the method. In particular, completeness can be
modularly proved by showing that the conclusions of each newly added inference
rule ensures that the corresponding conditions on frames hold. Some examples
are given in order to illustrate the use of the method.Comment: 15 pages, 1 figure. Preprint of the paper accepted to IJCAR 201
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
Formalization, Mechanization and Automation of G\"odel's Proof of God's Existence
G\"odel's ontological proof has been analysed for the first-time with an
unprecedent degree of detail and formality with the help of higher-order
theorem provers. The following has been done (and in this order): A detailed
natural deduction proof. A formalization of the axioms, definitions and
theorems in the TPTP THF syntax. Automatic verification of the consistency of
the axioms and definitions with Nitpick. Automatic demonstration of the
theorems with the provers LEO-II and Satallax. A step-by-step formalization
using the Coq proof assistant. A formalization using the Isabelle proof
assistant, where the theorems (and some additional lemmata) have been automated
with Sledgehammer and Metis.Comment: 2 page
A Fibred Tableau Calculus for BDI Logics
In [12,16] we showed how to combine propositional BDI logics using Gabbay's fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based decision procedure for the combined/fibred logics. To achieve this end we first outline with an example two types of tableau systems, (graph and path), and discuss why both are inadequate in the case of fibring. Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system KEM