Given an arbitrary intruder deduction capability, modeled as an inference system S and a protocol, we show how to compute an inference system b S such that the security problem for an unbounded number of sessions is equivalent to the deducibility of some message in b S. Then, assuming that S has some subformula property, we lift such a property to b S, thanks to a proof normalisation theorem. I...

Proof-theoretical notions and techniques, which are developed based on sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, ...

Any scientific discovery must include an epistemic process to gain knowledge of or to ascertain the existence of some empirical and/or logical entailments previously unknown or unrecognized. The epistemic operation of deduction in an epistemic process of an agent is to fred new and valid entailments logically from some premises which are known facts and/or assumed hypothesis. Automated theorem ...

In 1984 Milnor had shown how to deduce the Lie-Palais theorem on integration of infinitesimal actions of finite-dimensional Lie algebras on compact manifolds from general theory of regular Lie groups modelled on locally convex spaces. We show how, in the case of effective action, one can eliminate from Milnor’s argument the abstract Lie-Cartan theorem, making the deduction rather elementary. A ...

The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well deened formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides ba...

This paper discusses inference in computational semantics. We argue that state-of-the-art methods in rst-order theorem proving and model building are of direct relevance to inference for natural language processing. We support our claim by discussing the inferen-tial aspects of several higher discourse phenomena and reporting on an experiment where the induced deduction problems are solved by t...

The concept of fibring is extended to higher-order logics with arbitrary modalities and binding operators. A general completeness theorem is established for such logics including HOL and with the meta-theorem of deduction. As a corollary, completeness is shown to be preserved when fibring such rich logics. This result is extended to weaker logics in the cases where fibring preserves conservativ...

We claim that mathematical databases should be more than a collection of domains with associated theorems; in particular theorems should be stated as general as possible, that is independent of domains. A database then should be able to check whether such a general theorem holds in a particular domain. To this end we use a properties-based representation for both theorems and domains, and prese...

It is quite well understood that propositional logics are tightly connected to ordered algebras via algebraic completeness, and because of this connection proof theory is often useful in the algebraic context too. A prominent example is that one deductively proves the interpolation theorem for a given logic in order to derive the algebraic amalgamation property for the corresponding variety as ...

We develop an order-sorted higher-order calculus suitable for automatic theorem proving applications by extending the extensional simply typed lambda calculus with a higher-order ordered sort concept and constant overloading. Huet's well-known techniques for unifying simply typed lambda terms are generalized to arrive at a complete transformation-based uniication algorithm for this sorted calcu...