Dedukti has been proposed as a universal proof checker. It is a logical framework based on the λΠcalculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of rewriting. We present a shallow embedding into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deductio...

b b b b b b b b b b b b b b b b b b b Abstract The central problem in automated deduction is the explosive growth of search spaces when proof length increases. In this paper, a con-nectionist approach for learning search-control heuristics for automated deduction systems is presented. In particular, we show how folding architecture networks, a new type of neural networks capable of solving supe...

The well-known embedding of intuitionistic logic into classical modal logic means that intuitionistic logic can be viewed as a calculus of labelled deduction on multiple-conclusion sequents, where the labels are the Kripke worlds of the modal embedding. The corresponding natural deduction system constitutes a type system for programs using control operators such as letcc that capture the curren...

Existing search engines, with Google at the top, have many truly remarkable capabilities. Furthermore, constant progress is being made in improving their performance. But what is not widely recognized is that there is a basic capability which existing search engines do not have: deduction capability – the capability to synthesize an answer to a query by drawing on bodies of information which re...

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 has been shown to be logically equivalent to first-order logic, proofs in such systems are quite different and dramatically simpler wit...

In this paper, we consider multiplicative linear logic (MLL) from an automated deduction point of view. Linear logic is more expressive than classical and intuitionistic logic and has an undirectional character due to the particular treatment of negation and the absence of structural rules. Considering this new logical framework to make logic programming or programming with proofs (extracting p...

There are two basic approaches to automated verification. In model checking, the system is viewed as a graph representing possible execution steps. Properties are established by exploring or traversing the graph structure. In deduction, both the system and its putative properties are represented by formulas in a logic, and the resulting proof obligations are discharged by decision procedures or...

One of the most important open questions in reasoning research is how inductive reasoning and deductive reasoning are related. In an effort to address this question, we applied methods and concepts from memory research. We used 2 experiments to examine the effects of logical validity and premise-conclusion similarity on evaluation of arguments. Experiment 1 showed 2 dissociations: For a common ...