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### Full First-Order Sequent and Tableau Calculi With Preservation of Solutions and the Liberalized delta-Rule but Without Skolemization [article]

Claus-Peter Wirth
2009 arXiv   pre-print
We present a combination of raising, explicit variable dependency representation, the liberalized delta-rule, and preservation of solutions for first-order deductive theorem proving.  ...  Our main motivation is to provide the foundation for our work on inductive theorem proving, where the preservation of solutions is indispensable.  ...  preservation of solutions in full first-order logic.  ...

### , , and Non-Permutability of -Steps

Claus-Peter Wirth
2012 Journal of symbolic computation
and delta+-steps (according to Smullyan's classification), which is not visible with non-liberalized delta-rules and not serious with further liberalized delta-rules, such as the delta++-rule.  ...  Besides a careful presentation of the search for a proof of (lim+) with several pedagogical intentions, the main subject is to explain why the order of beta-steps plays such a practically important role  ...  I would also like to thank the lecturers and students of the course (Autexier et al., 2004/05)  ...

### 2015 EUROPEAN SUMMER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC LOGIC COLLOQUIUM '15 Helsinki, Finland August 3–8, 2015

2016 Bulletin of Symbolic Logic
When one attempts to develop the model theory of a logic generalizing first order logic, one runs into the problem that model theoretic properties of the logic like compactness, Löwenheim-Skolem Theorem  ...  Many interesting properties of mathematical structures and elements of such structures can not be expressed in first order logic.  ...  It is known that in Frege systems there are the trivial exponential upper bounds and only Ω(n 2 ) bounds of proof size and Ω(n) bounds of proof steps for tautologies with the size n [1].  ...

### Deduction (Dagstuhl Seminar 9709)

Wolfgang Bibel, Ulrich Furbach, Ryuzo Hasegawa, Mark Stickel
1997
During this seminar we had 41 talks, a panel, and a discussion how system implementors could cooperate.  ...  Dagstuhl, a place being developed exclusively for research activities in Computer Science, provides an excellent atmosphere for researchers to meet and exchange ideas.  ...  This means that we use a Skolemization for the term-and prefixvariables which is similar to some liberalized δ-rule in the classical tableau calculus.  ...

### Dagstuhl Report Deduction

Wolfgang Bibel, Ulrich Furbach, Ryuzo Hasegawa, Mark Stickel
unpublished
This means that we use a Skolemization for the term-and prefixvariables which is similar to some liberalized δ-rule in the classical tableau calculus.  ...  Melvin Fitting, City University of New York First-Order Modal Logics The talk consisted of a brief sketch of the complexities that must be addressed in a full treatment of first-order modal logic(s).  ...  We (dynamically) abstract the given clause set into a decidable fragment of first-order logic.  ...