Theorem proving for classical logic with partial functions by reduction to Kleene logic

2014 ◽  
Vol 27 (2) ◽  
pp. 509-548 ◽  
Author(s):  
Hans de Nivelle
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Partial Functions

scholarly journals Theorem Proving for Logic with Partial Functions Using Kleene Logic and Geometric Logic

10.29007/6qpn ◽  
2018 ◽  
Author(s):  
Hans De Nivelle
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Partial Functions ◽  
Geometric Logic ◽  
The Way

We introduce a theorem proving strategy for Partial Classical Logic (PCL) thatis based on geometric logic. The strategy first translates PCL theories into sets of Kleene formulas. After that, the Kleene formulas are translated into 3-valued geometric logic. The resulting formulas can be refuted by an adaptation ofgeometric resolution.The translation to Kleene logic does not only open the way to theorem proving, butit also sheds light on the relation between PCL, Kleene Logic, and classical logic.

The 10th IJCAR automated theorem proving system competition – CASC-J10

2021 ◽  
pp. 1-15
Author(s):  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Automated Theorem Proving ◽  
Fully Automatic

The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-J10 was the twenty-fifth competition in the CASC series. Twenty-four ATP systems and system variants competed in the various competition divisions. This paper presents an outline of the competition design, and a commentated summary of the results.

Classical Logic with Partial Functions

2011 ◽  
Vol 47 (4) ◽  
pp. 399-425 ◽  
Author(s):  
Hans de Nivelle
Keyword(s):  
Classical Logic ◽  
Partial Functions

scholarly journals Revising basic theorem proving algorithms to cope with the logic of partial functions

2014 ◽  
Vol 94 ◽  
pp. 238-252
Author(s):  
Cliff B. Jones ◽  
Matthew J. Lovert ◽  
L. Jason Steggles
Keyword(s):  
Theorem Proving ◽  
Partial Functions ◽  
Basic Theorem

scholarly journals Rewriting and Well-Definedness within a Proof System

10.29007/b7wc ◽  
2018 ◽  
Author(s):  
Issam Maamria ◽  
Michael Butler
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Term Rewriting ◽  
Proof System ◽  
Proof Technique ◽  
Partial Functions ◽  
Deductive Proof ◽  
Theorem Provers ◽  
Theoretical Foundations

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving between deduction and computation (i.e., rewriting) steps. If the logic of reasoning supports partial functions, it is necessary that rewriting copes with potentially ill-defined terms. In this paper, we provide a basis for integrating rewriting with a deductive proof system that deals with well-definedness. The definitions and theorems presented in this paper are the theoretical foundations for an extensible rewriting-based prover that has been implemented for the set theoretical formalism Event-B.

The CADE ATP System Competition — CASC

AI Magazine ◽  
2016 ◽  
Vol 37 (2) ◽  
pp. 99-101 ◽  
Author(s):  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Automated Theorem Proving ◽  
World Championship ◽  
Public Evaluation ◽  
The World ◽  
Fully Automatic

The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic automated theorem proving (ATP) systems for classical logic — the world championship for such systems. CASC provides a public evaluation of the relative capabilities of ATP systems, and aims stimulate ATP research towards the development of more powerful ATP systems. Over the years CASC has been a catalyst for impressive improvements in ATP.

Biomolecular theorem proving on a chip: a novel microfluidic solution to a classical logic problem

Lab on a Chip ◽  
2012 ◽  
Vol 12 (10) ◽  
pp. 1841 ◽  
Author(s):  
Seung Hwan Lee ◽  
Danny van Noort ◽  
Kyung-Ae Yang ◽  
In-Hee Lee ◽  
Byoung-Tak Zhang ◽  
...  
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Logic Problem

Methods and clinical applications in nuclear cardiology: a position statement

2002 ◽  
Vol 41 (01) ◽  
pp. 3-13 ◽  
Author(s):  
M. Schäfers
Keyword(s):  
Nuclear Cardiology ◽  
Clinical Medicine ◽  
Imaging Techniques ◽  
Cost Savings ◽  
Cost Benefit ◽  
Position Statement ◽  
Electron Beam Tomography ◽  
Partial Functions ◽  
Cost Benefit Ratio ◽  
Medicine Today

SummaryNuclear cardiological procedures have paved the way for non-invasive diagnostics of various partial functions of the heart. Many of these functions cannot be visualised for diagnosis by any other method (e. g. innervation). These techniques supplement morphological diagnosis with regard to treatment planning and monitoring. Furthermore, they possess considerable prognostic relevance, an increasingly important issue in clinical medicine today, not least in view of the cost-benefit ratio.Our current understanding shows that effective, targeted nuclear cardiology diagnosis – in particular for high-risk patients – can contribute toward cost savings while improving the quality of diagnostic and therapeutic measures.In the future, nuclear cardiology will have to withstand mounting competition from other imaging techniques (magnetic resonance imaging, electron beam tomography, multislice computed tomography). The continuing development of these methods increasingly enables measurement of functional aspects of the heart. Nuclear radiology methods will probably develop in the direction of molecular imaging.

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