We describe a collaborative effort in which the HOL4 theorem prover is being used to formally verify properties of a structure within the Large Hadron Collider (LHC) machine protection system at the European Organization for Nuclear Research (CERN). This structure, known as Successive Running Sums (SRS), generates the primary input to the decision logic that must initiate a critical action by t...

Deduction Modulo implements Poincaré’s principle by identifying deduction and computation as different paradigms and making their interaction possible. This leads to logical systems like the sequent calculus or natural deduction modulo. Even if deduction modulo is logically equivalent to first-order logic, proofs in such systems are quite different and dramatically simpler with one cost: cut el...

It is widely accepted that to extend the eeectiveness of information disclosure beyond the limitations of current empirically-based retrieval systems, some notion of document semantics has to be incorporated into the retrieval mechanism. A recent approach to bringing semantics into play is to found the retrieval mechanism on the notion of logical inference. In this paper, we build on this appro...

Reasoning in the activity of evaluating arguments. All arguments involve the claim that one or more propositions (the premise) provide some grounds for accepting another proposition (the conclusion). Philosophers have sorted arguments into two broad categories – induction and deduction – based on the nature of the relationship between premise and conclusion. Valid deductive arguments involve th...

n a The aim of this paper is at analyzing from various points of view the relationships betwee bduction and deduction. In particular, we consider a meta-level definition of abduction in l d terms of deduction, similar to various definitions proposed in the literature, and an object-leve efinition in which abductive conclusions are expressed as a logical consequence of the obser. T vations and o...

After the work of Gri n in 1990, there have been many works to extend the Curry-Howard isomorphism for classical logic. Most of these research uses sequent calculus with multiple conclusions. In this paper, we introduce a new natural deduction formulation with one conclusion for implicational classical logic. The idea of the formulation is based on proof by \case analysis". It is natural and ca...

Based on natural deduction, Pure Type Systems (PTS) can express a wide range of type theories. In order to express proof-search in such theories, we introduce the Pure Type Sequent Calculi (PTSC) by enriching a sequent calculus due to Herbelin, adapted to proof-search and strongly related to natural deduction. PTSC are equipped with a normalisation procedure, adapted from Herbelin’s and defined...

Many existing search engines do not have an important capability, the capability to deduce an answer to a query based on information which reside in various parts of documents. The levels-of-processing theory proposes that there are many ways to process and code information and thus the knowledge representation used as surrogate to documents are qualitatively different. The capability of deduct...

The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's. First a family of propositional logical systems is considered, which is obtained by gradually addin...