@Inproceedings{Poole-Preferring-Most-Specific-1985, year={1985}, author={Poole, David L.}, title={On the Comparison of Theories: Preferring the Most Specific Explanation}, note={In \cite[\PP{144}{147}]{ijcai9}. \url{http://ijcai.org/Past%20Proceedings/IJCAI-85-VOL1/PDF/026.pdf}}, } @Book{wirth-herbrand-encyclopedia-SEKI, year={2015}, author={Wirth, Claus-Peter}, title={{Herbrand's Fundamental Theorem} --- an encyclopedia article}, publisher={{SEKI Publications}}, series={{SEKI-Report SR--2015--01 (ISSN 1437--4447)}}, note={\PPcount{ii+16}, \url{http://arxiv.org/abs/1503.01412}}, } @Article{FS+15b, year={2015}, author={Furbach, Ulrich and Schon, Claudia and Stolzenburg, Frieder and Weis, Karl-Heinz and Wirth{\protectedwirthindex}, Claus-Peter}, title={{The RatioLog Project --- Rational Extensions of Logical Reasoning}}, journal={{KI -- K\ue nstliche Intelligenz (German J. of Artificial Intelligence), \springerverlag}}, volume={29}, pages={1--7}, note={Published online \Jun\,05, 2015. \url{http://dx.doi.org/10.1007/s13218-015-0377-9}. Also in \url{http://arxiv.org/abs/1503.06087}}, } @Book{SR--2009--01, year={2014}, author={Wirth, Claus-Peter and Siek{\-}mann, J{\"o}rg and Benz{\-}m{\"u}ller, {\mbox{Ch}}ristoph and Autexier, Serge}, title={Lectures on {\herbrandname} as a Logician}, publisher={{SEKI Publications}}, series={{SEKI-Report SR--2009--01 (ISSN 1437--4447)}}, note={\Rev\,\edn\ \May\,2014, \PPcount{ii+82}, {\url{http://arxiv.org/abs/0902.4682}}}, } @Proceedings{IFIP-1974, year={1974}, editor={Rosenfeld, Jack L.}, title={{\Proc\ of the Congress of the \Int\ Federation for Information Processing (IFIP), Stockholm (Sweden), \Aug\,5--10, 1974}}, publisher={\northholland}, } @InProceedings{Kow74, year={1974}, author={Kowalski, Robert A.}, title={Predicate Logic as a Programming Language}, note={In \cite[\PP{569}{574}]{IFIP-1974}}, } @Article{wgjsc, year={1994}, author={Wirth, Claus-Peter and Gramlich, Bernhard}, title={A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications}, journal={{\jscname}}, volume={17}, pages={51--90}, publisher={\academicpress}, note={\url{http://dx.doi.org/10.1006/jsco.1994.1004}, \www\url{/p/jsc94}}, abstract={We study algebraic specifications given by finite sets R of positive/negative-conditional equations (i.e.\ universally quantified first-order implications with a single equation in the succedent and a conjunction of positive and negative (i.e.\ negated) equations in the antecedent). The class of models of such a specification R does not contain in general a minimum model in the sense that it can be mapped to any other model by some homomorphism. We present a constructor-based approach for assigning appropriate semantics to such specifications. We introduce two syntactic restrictions: firstly, for a condition to be fulfilled we require the evaluation values of the terms of the negative equations to be in the constructor sub-universe which contains the set of evaluation values of all constructor ground terms; secondly, we restrict the constructor equations to have ``Horn''-form and to be ``constructor-preserving''. A reduction relation for R is defined, which allows to generalize the fundamental results for positive-conditional rewrite systems, which does not need to be noetherian or restricted to ground terms, and which is monotonic \wrt\ consistent extension of the specification. Under the assumption of confluence, the factor algebra of the ground term algebra modulo the congruence of the reduction relation is a minimal model which is (beyond that) the minimum of all models that do not identify more constructor ground terms than necessary. To achieve decidability of reducibility we define several kinds of compatibility of R with a reduction ordering and present a complete critical-pair test a la Knuth--Bendix for the confluence of the reduction relation.}, } @Book{wirthdiss, year={1997}, author={Wirth, Claus-Peter}, title={Positive/Negative-Conditional Equations: A Constructor-Based Framework for Specification and Inductive Theorem Proving}, publisher ={{Verlag Dr.\ Kova\v c, Hamburg}}, volume={31}, series={{Schriftenreihe Forschungsergebnisse zur Informatik}}, note={\PhDthesis, \uniKLshort, {ISBN 386064551X}, {\www\url{/p/diss}}}, abstract={{The subject of this thesis is clausal inductive theorem proving on the basis of specifications with constructor-based positive/negative-conditional equations. Proving inductive theorems is crucial for reasoning about computer programs. Since formal methods are indispensable to verifying safety-critical algorithms, it is to be expected that more or less automated inductive theorem proving will gain economic significance in the nearer future. \par Positive/negative-conditional equations are universally quantified first-order implications with a single equation in the succedent and a conjunction of positive and negative (i.e. negated) equations in the antecedent. They are convenient for writing first-order functional specifications, which can also be seen as programs. \par With the help of a constructor-based approach an appropriate semantics is assigned to algebraic specifications given by positive/negative-conditional equations. Furthermore, a reduction relation for positive/negative-conditional rules is defined, for which the fundamental results for positive-conditional rewrite systems can be sustained. It is important that the presented notions of inductive validity are monotonic w.r.t. consistent extension of the specification. On this basis, an inference system for clausal theorem proving w.r.t. various kinds of inductive validity is developed. The constructor-based approach turns out to be well-suited for inductive theorem proving, even in the presence of partially defined and non-terminating functions.\par}}, } @Article{wirth-jsc, Year={2009}, Author={Wirth, Claus-Peter}, Title={Shallow Confluence of Conditional Term Rewriting Systems}, Journal={{\jscname}}, volume={44}, pages={69--98}, note={\url{http://dx.doi.org/10.1016/j.jsc.2008.05.005}}, } @Proceedings{fourteenthKRfourteen, year={2014}, editor={Baral, Chitta and De Giacomo, Giuseppe and Eiter, Thomas}, title={{\fourteenthKRfourteen}}, publisher={\aaaipress}, note={\url{http://www.aaai.org/Library/KR/kr14contents.php}}, } @InProceedings{Wirth_Stolzenburg_Specificity_KR2014, year={2014}, author={Wirth, Claus-Peter and Stolzenburg, Frieder}, title={\poolename's Specificity Revised}, note={In \cite[\PP{168}{177}]{fourteenthKRfourteen}. Short version of \cite{Wirth_Stolzenburg_Specificity_2013}}, } @Book{wirth-heijenoort-SEKI, year={2014}, author={Wirth, Claus-Peter}, title={{\herbrandsfundamentaltheorem:} The Historical Facts and their Streamlining}, publisher={{SEKI Publications}}, series={{SEKI-Report SR--2014--01 (ISSN 1437--4447)}}, note={\PPcount{ii+47}, \url{http://arxiv.org/abs/1405.6317}}, } @Book{Prolog, year={2003}, author={Clocksin, William F. and Mellish, Christopher S.}, title={{Programming in \PROLOG}}, publisher={{\springerverlag}}, note={\nth 5\,\edn\ (\nth 1\,\edn\,1981)}, } @article{Modgil_Prakken_ASPIC_Tutorial_2014, year={2014}, author={Sanjay Modgil and Henry Prakken}, title={The {{\em ASPIC}\/$^+$} Framework for Structured Argumentation: a tutorial}, journal={Argument {\&} Computation}, volume={5}, pages={31--62}, note={\url{http://dx.doi.org/10.1080/19462166.2013.869766}}, } @Article{Furbach-etal-AR-in-NL-Question-Answering-2010, year={2010}, author={Furbach, Ulrich and Gl{\"o}ckner, Ingo and Pelzer, Bj{\"o}rn}, title={An Application of Automated Reasoning in Natural-Language Question Answering}, journal={{\artificialintelligencecommunicationsname}}, volume={23}, pages={241--265}, } @Inproceedings{Besnard_etal_A_Conditional_Argumentation_Framework_2013, year={2013}, author={Philippe Besnard and {\'E}ric Gr{\'e}goire and Badran Raddaoui}, title={A Conditional Logic-Based Argumentation Framework}, note={In \cite[\PP{44}{56}]{seventhSUMthirteen}. \url{http://dx.doi.org/10.1007/978-3-642-40381-1_4}}, } @Proceedings{seventhSUMthirteen, year={2013}, editor={Weiru Liu and V. S. Subrahmanian and Jef Wijsen}, title={{\Proc\ \nth 7 \Int\ \Conf\ on Scalable Uncertainty Management (SUM 2013), Washington (DC), \Sep\,16--18, 2013}}, publisher={{\springerverlag}}, series={Lecture Notes in Computer Science}, number={8078}, } @Phdthesis{herbrand-PhD, year={1930}, author={Herbrand, Jacques}, title={{\herbrandPhDtitle}}, school={Universit\'e de Paris}, note={No.\,d'ordre\,2121, S\'erie\,A, No.\,de\,S\'erie\,1252 --- Imprimerie J. Dziewulski, Varsovie --- \Univ\ de \Paris. \ Also in Prace \WarsawScientificSocietyIII\ Nauk Matematyczno-Fizychnych, Nr.\,33, \Warszawa.}, } @Book{handbook-of-the-history-of-logic, year={2004\ff}, editor={Gabbay, Dov and Woods, John}, title={Handbook of the History of Logic}, publisher={\northholland}, } @incollection{herbrand-handbook, year={2009}, author={Wirth, Claus-Peter and Siek{\-}mann, J{\"o}rg and Benz{\-}m{\"u}ller, {\mbox{Ch}}ristoph and Autexier, Serge}, title={\herbrandname: Life, Logic, and Automated Deduction}, note={In \cite[\Vol\,5: Logic from \russell\ to \church, \PP{195}{254}]{handbook-of-the-history-of-logic}}, } @article{Besnard-Hunter-Logic-Based-Theory-of-Deductive-Arguments-2001, year={2001}, author={Philippe Besnard and Anthony Hunter}, title={A Logic-Based Theory of Deductive Arguments}, journal={{\artificialintelligencename}}, volume={128}, pages={203--235}, note={Received \Dec\,8, 2000. \url{http://dx.doi.org/10.1016/S0004-3702(01)00071-6}}, } @Article{wirth-heijenoort, year={2012}, author={Wirth, Claus-Peter}, title={{\herbrandsfundamentaltheorem} in the Eyes of {\heijenoortname}}, journal={{\logicauniversalisname}}, volume={6}, pages={485--520}, note={Received \Jan\,12, 2012. Published online \Jun\,22, 2012, \url{http://dx.doi.org/10.1007/s11787-012-0056-7}}, } @Book{Wirth_Stolzenburg_Specificity_2013, year={2013}, author={Wirth, Claus-Peter and Stolzenburg, Frieder}, title={\poolename's Specificity Revised}, publisher={{SEKI Publications}}, series={{SEKI-Report SR--2013--01 (ISSN 1437--4447)}}, note={\PPcount{ii+34}, \url{http://arxiv.org/abs/1308.4943}}, } @Article{Gelfond_Przymusinska_1990, year={1990}, author={Michael Gelfond and Halina Przymusinska}, title={Formalization of Inheritance Reasoning in Autoepistemic Logic}, journal={\fundamentainformaticaename}, publisher={IOS Press}, volume={XIII}, pages={403--443}, } @Article{Simari-Loui-Defeasible-Reasoning-1992, year={1992}, author={Simari, Guillermo R. and Loui, Ronald P.}, title={A Mathematical Treatment of Defeasible Reasoning and its Implementation}, journal={\artificialintelligencename}, volume={53}, pages={125--157}, note={Received \Feb\,1990, \rev\,\Apr\,1991}, } @Book{lambert-1764, year={1764}, author={Lambert, Johann Heinrich}, title={{Neues Organon oder Gedanken \ue ber die Erforschung und Bezeichnung des Wahren und dessen Unterscheidung von Irrthum und Schein.}}, publisher={Johann Wendler, \Leipzig}, note={{\Vol\,I\ (Dianoiologie oder die Lehre von den Gesetzen de\es\ Denken\es, Alethiologie oder Lehre von der Wahrheit) (\url{http://books.google.de/books/about/Neues_Organon_oder_Gedanken_Uber_die_Erf.html?id=ViS3XCuJEw8C}) \& \Vol\,II (Semiotik oder Lehre von der Bezeichnung der Gedanken und Dinge, Ph\ae nomenologie oder Lehre von dem Schein) (\url{http://books.google.de/books/about/Neues_Organon_oder_Gedanken_%C3%BCber_die_Er.html?id=X8UAAAAAcAAj})\@. \ Facsimile reprint by \olmsverlag, 1965, with a German introduction by \hanswernerarndtname}}, } @InProceedings{DS96, year={1996}, author={Dung, Phan Minh and Son, Tran Cao}, title={An Argumentation-Theoretic Approach to Reasoning with Specificity}, Xnote={In \cite[\PP{506}{517}]{fifthKRninetysix}}, crossref={fifthKRninetysix}, pages={506-517} } @Proceedings{fifthKRninetysix, year={1996}, editor={Luigia Carlucci Aiello and Jon Doyle and Stuart C. Shapiro}, title={\Proc\ \nth 5 \Int\ \Conf\ on Principles of Knowledge Representation and Reasoning, 1996, \Nov\,5--8, Cambridge (MA)}, booktitle={\Proc\ \nth 5 \Int\ \Conf\ on Principles of Knowledge Representation and Reasoning, 1996, \Nov\,5--8, Cambridge (MA)}, publisher={\morgankaufmann}, } @InProceedings{BG97b, year={1997}, author={Salem Benferhat and Laurent Garcia}, title={A Coherence-Based Approach to Default Reasoning}, Xnote={In \cite[\PP{43}{57}]{}}, note={\url{http://dx.doi.org/10.1007/BFb0035611}}, crossref={DBLP:conf/ecsqaru/1997}, pages={43-57} } @Proceedings{DBLP:conf/ecsqaru/1997, year={1997}, editor={Gabbay, Dov and Rudolf Kruse and Nonnengart, Andreas and Ohlbach, Hans-J{\"u}rgen}, title={\Proc\ \nth 1 \Int\ Joint \Conf\ on Qualitative and Quantitative Practical Reasoning, 1997, \Jun\,9--12, Bad Honnef (Germany)}, booktitle={\Proc\ \nth 1 \Int\ Joint \Conf\ on Qualitative and Quantitative Practical Reasoning, 1997, \Jun\,9--12, Bad Honnef (Germany)}, publisher={\springerverlag}, series={Lecture Notes in Computer Science}, number={1244}, } @Article{ Chesnevar-etal-Relating-Deafeasible-2003, year = {2003}, author = {Ches{\~n}evar, Carlos I. and Dix, J{\"u}rgen and Stolzenburg, Frieder and Simari, Guillermo R.}, title = {Relating Defeasible and Normal Logic Programming through Transformation Properties}, journal = {\tcsname}, volume = {290}, pages = {499--529}, note = {Received \Jan\,8, 2001; \rev\ \Nov\,9, 2001. \url{http://dx.doi.org/10.1016/S0304-3975(02)00033-6}} } @Article{ Garcia-Simari-Defeasible-2004, year = {2004}, author = {Garc{\'\i}a, Alejandro J. and Simari, Guillermo R.}, title = {Defeasible Logic Programming: An Argumentative Approach}, journal = {Theory and Practice of Logic Programming, \cambridgeunipress}, volume = {4}, pages = {95--138} } @Proceedings{ijcai9, year={1985}, editor={Joshi, Aravind}, title={{\Proc\ \nth 9 \IJCAIname\ (\IJCAI), 1985, \Aug\,18--25, \LA}}, booktitle={{\Proc\ \nth 9 \IJCAIname\ (\IJCAI), 1985, \Aug\,18--25, \LA}}, publisher={\morgankaufmann}, note={{\url{http://ijcai.org/Past%20Proceedings}}}, } @Article{ Stolzenburg-etal-Computing-Specificity-2003, year = {2003}, author = {Stolzenburg, Frieder and Garc{\'\i}a, Alejandro J. and Ches{\~n}evar, Carlos I. and Simari, Guillermo R.}, title = {Computing Generalized Specificity}, booktitle = {Computing Generalized Specificity}, journal = {\janclname}, volume = {13}, pages = {87--113}, note = {\url{http://www.tandfonline.com/doi/abs/10.3166/jancl.13.87-113}} } @Book{ writing-mathematics, year = {1987}, author = {Leonard Gillman}, title = {Writing Mathematics Well}, publisher = {The Mathematical Association of America} } @InCollection{Prakken-Vreeswijk-Logics-for-Defeasible-Argumentation-2002, year={2002}, author={Henry Prakken and Gerhard Vreeswijk}, title={Logics for Defeasible Argumentation}, note={In \cite[\PP{218}{319}]{handbookofphilosophicallogicsecondedn}}, } @Book{handbookofphilosophicallogicsecondedn, year={2002}, editor={Gabbay, Dov}, title={Handbook of Philosophical Logic}, publisher={\kluwer}, note={\nth 2\,\edn}, } @article{Dung_Acceptability_of_Arguments_1995, year={1995}, author={Dung, Phan Minh}, title={On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games}, journal={Artificial Intelligence}, volume={77}, pages={321--358}, note={\url{http://dx.doi.org/10.1016/0004-3702(94)00041-X}}, } @InProceedings{Kern-Isberner-Thimm-Ranking-Semantics-2012, year={2012}, author= {Gabriele Kern-Isberner and Matthias Thimm}, title={A Ranking Semantics for First-Order Conditionals}, note={\cite[\PP{456}{461}]{twentiethECAItwelve}. \url{http://dx.doi.org/10.3233/978-1-61499-098-7-456}}, } @Proceedings{twentiethECAItwelve, year={2012}, editor={Luc De Raedt and Christian Bessi{\`e}re and Didier Dubois and Patrick Doherty and Paolo Frasconi and Fredrik Heintz and Peter J. F. Lucas}, title={{\Proc\ \nth{20} \ECAIname\ (ECAI), \Aug\,27--31, 2012, Montepellier, France}}, publisher={IOS Press}, series={Frontiers in Artificial Intelligence and Applications}, number={242}, note={\url{http://ebooks.iospress.nl/volume/ecai-2012}}, }