Early History and Perspectives of Automated Deduction

Abstract

Abstract. With this talk we want to pay tribute to the late Professor Gerd Veenker who deserves the historic credit of initiating the formation of the German AI community. We present a summary of his scientific contributions in the context of the early approaches to theorem proving and, against this background, we point out future perspectives of Automated Deduction.

Artificial Intelligence in a historical perspective

“…Thereby I try to avoid too much overlap with the contents of two comparable articles published earlier by this author [13,15], so that the three articles can to some extent be regarded as complementary.…”

“…The two years 1936-1938 he spent in Princeton, NJ, studying and obtaining a doctorate under Alonzo Church , another hero in mathematical logic, a discipline which is one of the founding corner-stones of AI (and of CS for that matter) [50]. Among a lot of other work on a variety of topics (including statistics, cryptography, the first detailed design of a program-stored computer, program verification, morphogenesis 14 ), 15 Turing in 1950 published his famous Turing Test paper [67] which has remained sort of a manifest for AI since then. 16 It is worth noting that Turing met Zuse in a colloquium which took place in Göttingen in 1947 [20,26].…”

Non-Clausal Multi-ary α-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

“…The focus of this paper is on the resolution principle and the theoretical soundness and completeness of this resolution-based automated deduction, not on the concrete algorithms or search strategies for implementation. For resolution-based automated reasoning in lattice-valued logic based on LIA, 1) it is more complex than that in classical logic from the logical point of view; 2) it will be not that straightforward either in determining or search which group of generalized literals could be α-resoluble, that is, resoluble at a truth-value level α, or determining at least how many generalized literals can be chosen in the α-resolution group once given a truth-value level α; 3) although the resolution process can borrow the similar ideas from classical logic, it becomes more complex due to the more complex generalized literals involved in the resolution and also the fact that it allows the choice of various truth-value level resolution (different from the only case of α=O in classical logic).…”

“…This paper is a continuation and extension of the work in [25][26][27][28][29][30][31][32][33] , the binary α-resolution principle introduced in [25,26] for L(X) is extended to multi-ary α-generalized resolution principle in different ways as follows: (1) the resolution is based on general generalized clauses which is constructed by the generalized literals and logical connectives ″∨, ∧, ′, →, ↔″, instead of the generalized clause containing only ″ ′, →″ in [25,26]. This, in essential, is a non-clausal resolution; (2) the set of the generalized clauses, which is a complex logical formula, are not necessary to be transformed into the GCNF; (3) the above extended binary α-generalized resolution is further extended into multi-ary α-generalized resolution, i.e., extends the α-generalized resolution pair composed of two generalized literals to the α-generalized resolution group composed of multiple generalized literals based on the work in [24].…”

“…The resolution principle is one simple but efficient inference principle, and the resolution calculus is sound and complete in the Boolean logic system. Since its introduction by Robinson in 1965 [1] , resolution-based automated reasoning has been extensively studied with the attempt to find natural and efficient proof systems to supporting a wide spectrum of computational tasks [2][3][4][5] .…”