[PDF] Top 20 Automated theorem-proving in non-classical logics

... For example, the stn·ct implication of the modal systems of [Lewis 18] were motivated by Lewis as presenting a better account of implication, in that strict implication avoided several o[r] ... See full document

... The starting point of this thesis was the combination of two results: the first is Goldblatt’s topo- logical proofs of the Rasiowa-Sikorski Lemma for distributive lattices and Heyting algebras [30]. The second is the ... See full document

... detachment theorem, hence entailment cannot be computed by theoremhood, we need to use sequents of the form α ⇒ β to formalize the axiomatization of distributive modal ... See full document

... with non-classical logics of even higher complexity as modal and intuitionistic logics which typically are PSPACE -complete and where expo- nential lower bounds are known for Frege and even ... See full document

... (theorem proving), circuit design (program verification) and medical diagnosis (expert systems) ...applying automated reasoning and logic to (social) choice theory are, how- ever, not less successful ... See full document

... Automated theorem proving is a collection of techniques to deal with mathematical theorems using a computer ...different logics including temporal ...consider automated temporal ... See full document

... no-cloning theorem, stating that unknown pure quan- tum states cannot be copied unless they are orthogo- nal [12, ...broadcasting theorem for mixed states ...quantum logics with a conditional prob- ... See full document

... of proof systems and determine whether proofs can be efficiently translated be- tween different formalisms. In this paper our results will employ both of these paradigms. While the bulk of research in proof complexity ... See full document

... have seen two fundamentally different techniques implementing the high school method, which is syntax-directed; one which requires construction of highly specialised strategies, and one which relies on judgements to ... See full document

... of limits, convergence, power series representations and so on, using these to obtain proofs of basic proper- ties, and then setting up automated tactics which can use the basic facts to deal with the identities ... See full document

... Let us mention that the separation of complexity classes is not the only motivation for studying lengths of proofs. In particular concerning strong sys- tems such as Frege and its extensions there is a fruitful ... See full document

... Tennenbaum’s Theorem is not one of ...Incompleteness Theorem pa 6` Con( pa ) not being at all clear that arithmetic is consistent from the start; of course, pa +Con( pa ) `Con( pa ), but then pa +Con( pa ) ... See full document

... on the nonlinear term f is not necessary, this point is very important because we can directly prove existence of positive solution and negative solution by using Rabinowitz’s mountain pass theorem. That is, the ... See full document

... Liquid Haskell is not the first attempt to bring theorem prov- ing to Haskell. Zeno [Sonnex et al. 2012] generates proofs by term rewriting and Halo [Vytiniotis et al. 2013] uses an ax- iomatic encoding to verify ... See full document

... of the implicit function theorem approach for proving Frechet differentiability and continuity of these non-linear operators does not seem to have been appreciated in the literature wher[r] ... See full document

... since non-autonomous ODEs can be brought into autonomous form by augmenting the dynamics with t 0 = ...Certain non-polynomial systems of ODEs can likewise be brought into polynomial form by introducing ... See full document

... tent, ill" at least one of its disjuncts is consistent, we only need all algorithm for.deciding consistency of finite sets of literals atomic formulas or negated atomic formulas S.. ing [r] ... See full document

... Normal Form Theorem Proving for the Lambek Calculus N o r m a l F o r m T h e o r e m P r o v i n g f o r t h e L a m b e k C a l c u l u s ~ M a r k H e p p l e C e n t r e f o r C o g n i t i v e S[.] ... See full document

... When the abstraction of the two subjects sort out and write down important information from the theorem, the female subject also sketched a triangle. Generalization carried out by the male subject by taking any ... See full document

... KeYmaera 3. KeYmaera 3 [PQ08] is the previous generation theorem prover for differential dynamic logic d L. Unlike its successor KeYmaera X, the older KeYmaera 3 directly implements a sequent calculus for ... See full document