Abstract Many problems in mathematics and computer science involve summations. We present a procedure that automatically proves equations involving finite summations, inspired by the theory of holonomic sequences. The is designed to be interleaved with activities higher-order automatic theorem prover. It performs an induction solves step, leaving base cases

We show that sometimes partial deduction produces poor program specializations because of its limited ability in (i) dealing with conjunctions of recursively deened predicates, (ii) combining partial evaluations of alternative computations, and (iii) taking into account unii-cation failures. We propose to extend the standard partial deduction technique by using versions of the deenition rule an...

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...

Recently, partial deduction of logic programs has been extended to conceptually embed folding. To this end, partial deductions are no longer computed of single atoms, but rather of entire conjunctions; Hence the term “conjunctive partial deduction”. Conjunctive partial deduction aims at achieving unfold/fold-like program transformations such as tupling and deforestation within fully automated p...

Deduction graphs [3] provide a formalism for natural deduction, where the deductions have the structure of acyclic directed graphs with boxes. The boxes are used to restrict the scope of local assumptions. Proof nets for multiplicative exponential linear logic (MELL) are also graphs with boxes, but in MELL the boxes have the purpose of controlling the modal operator !. In this paper we study th...

Associative-commutative equational reasoning is known to be highly complex for theorem proving. Hence, it is very important to focus deduction by adding constraints, such as uniication and ordering, and to deene eecient strategies, such as the basic requirements a la Hullot. Constraints are formulas used for pruning the set of ground instances of clauses deduced by a theorem prover. We propose ...

In this article we argue in favour of Natural Deduction Systems as a basis for formal proof explanations. We illustrate our choice presenting a Natural Deduction for ALCQI and use it to help explain UML reasoning.

The normalization theorem for the system of extended natural deduction will be proved as a consequence of the cut-elimination theorem, by using the connections between the system of extended natural deduction and a standard system of sequents.

The goal of researchers in automated deduction is to develop methods and tools to assist mathematicians, scientists, and engineers with some of the deductive aspects of their work. In contrast to other symbolic computation systems, the core methods in automated deduction focus on searching for proofs and counterexamples. Automated deduction can be applied to wide-ranging problems in nearly any ...