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...

In this paper we investigate, for intuitionistic implicational logic, the relationship between normalization in natural deduction and cut-elimination in a standard sequent calculus. First we identify a subset of proofs in the sequent calculus that correspond to proofs in natural deduction. Then we define a reduction relation on those proofs that exactly corresponds to normalization in natural d...

A method of deductive learning is proposed to con trol deductive inference Our goal is to improve prob lem solving time by experience when that experience monotonically adds knowledge to the knowledge base Accumulating and exploiting experience are done by the schemes of knowledge migration and knowledge shadowing Knowledge migration generates speci c migrated rules from general migrating rules...

A new predicate calculus deduction system based on production rules is pro. Logical deduction is a basic activity in many artificial intelligence Al systems.ideas that support many of the useful applications of artificial intelligence. Many Rule-Based Systems Are Deduction Systems. One of the most important aspects of rule-based systems is the. For instance, in deduction systems, forward.They a...

We studied the coordination of cooperative advertisement in a manufacturer–retailer supply chain when the manufacturer offers price deductions to customers.With a price sensitive market, the expected demand with cooperative advertising and price deduction is demonstrated. When the manufacturer is a leader, we obtained the optimal national brand name investment, local advertisement and associate...

The performance of an automated forward deduction system is crucial to its applicability. Since a forward deduction system working for discovery has no explicitly specified proposition or theorem given previously as goal, it often deduces many redundant intermediates, i.e., instances of those that have previously deduced. Therefore, how to reduce redundant intermediates is a general and difficu...

We present rst steps towards fully automated deduction that merely requires the user to submit proof problems and pick up results. Essentially, this necessitates the automation of the crucial step in the use of a deduction system, namely choosing and connguring an appropriate search-guiding heuristic. Furthermore, we motivate why learning capabilities are pivotal for satisfactory performance. T...