9,851 research outputs found
Theorem proving with built-in hybrid theories
A growing number of applications of automated reasoning exhibits the necessity of flexible deduction systems. A deduction system should be able to execute inference rules which are appropriate to the given problem. One way to achieve this behavior is the integration of different calculi. This led to so called hybrid reasoning [22, 1, 10, 20] which means the integration of a general purpose foreground reasoner with a specialized background reasoner. A typical task of a background reasoner is to perform special purpose inference rules according to a built-in theory. The aim of this paper is to go a step further, i.e. to treat the background reasoner as a hybrid system itself. The paper formulates sufficient criteria for the construction of complete calculi which enable reasoning under hybrid theories combined from sub-theories. For this purpose we use a generic approach described in [20]. This more detailed view on built-in theories is not covered by the known general approaches [1, 3, 6, 20] for building in theories into theorem provers. The approach is demonstrated by its application to the target calculi of the algebraic translation [9] of multi-modal and extended multi-modal [7] logic to first-order logic
Tool support for reasoning in display calculi
We present a tool for reasoning in and about propositional sequent calculi.
One aim is to support reasoning in calculi that contain a hundred rules or
more, so that even relatively small pen and paper derivations become tedious
and error prone. As an example, we implement the display calculus D.EAK of
dynamic epistemic logic. Second, we provide embeddings of the calculus in the
theorem prover Isabelle for formalising proofs about D.EAK. As a case study we
show that the solution of the muddy children puzzle is derivable for any number
of muddy children. Third, there is a set of meta-tools, that allows us to adapt
the tool for a wide variety of user defined calculi
Actor Network Procedures as Psi-calculi for Security Ceremonies
The actor network procedures of Pavlovic and Meadows are a recent graphical
formalism developed for describing security ceremonies and for reasoning about
their security properties. The present work studies the relations of the actor
network procedures (ANP) to the recent psi-calculi framework. Psi-calculi is a
parametric formalism where calculi like spi- or applied-pi are found as
instances. Psi-calculi are operational and largely non-graphical, but have
strong foundation based on the theory of nominal sets and process algebras. One
purpose of the present work is to give a semantics to ANP through psi-calculi.
Another aim was to give a graphical language for a psi-calculus instance for
security ceremonies. At the same time, this work provides more insight into the
details of the ANPs formalization and the graphical representation.Comment: In Proceedings GraMSec 2014, arXiv:1404.163
Automated Synthesis of Tableau Calculi
This paper presents a method for synthesising sound and complete tableau
calculi. Given a specification of the formal semantics of a logic, the method
generates a set of tableau inference rules that can then be used to reason
within the logic. The method guarantees that the generated rules form a
calculus which is sound and constructively complete. If the logic can be shown
to admit finite filtration with respect to a well-defined first-order semantics
then adding a general blocking mechanism provides a terminating tableau
calculus. The process of generating tableau rules can be completely automated
and produces, together with the blocking mechanism, an automated procedure for
generating tableau decision procedures. For illustration we show the
workability of the approach for a description logic with transitive roles and
propositional intuitionistic logic.Comment: 32 page
Algebraic Properties of Qualitative Spatio-Temporal Calculi
Qualitative spatial and temporal reasoning is based on so-called qualitative
calculi. Algebraic properties of these calculi have several implications on
reasoning algorithms. But what exactly is a qualitative calculus? And to which
extent do the qualitative calculi proposed meet these demands? The literature
provides various answers to the first question but only few facts about the
second. In this paper we identify the minimal requirements to binary
spatio-temporal calculi and we discuss the relevance of the according axioms
for representation and reasoning. We also analyze existing qualitative calculi
and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia
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