@techreport{RISC5885,
author = {David M. Cerna},
title = {{Evaluation of the VL Logic (342.208-9) 2018W End of Semester Questionnaire}},
language = {english},
abstract = {In this technical report we cover the choice of layout and intentions behind our end of the semester questionnaire as well as our interpretation of student answers, resulting statistical analysis, and inferences. Our questionnaire is to some extent free-form in that we provide instructions concerning the desired content of the answers but leave the precise formulation of the answer to the student. Our goal, through this approach, was to gain an understanding of how the students viewed there own progress and interest in the course without explicitly guiding them. Towards this end, we chose to have the students draw curves supplemented by short descriptions of important features. We end with a discussion of the benefits and downsides of such a questionnaire as well as what the results entail concerning future iterations of the course. },
year = {2019},
month = {Feburary},
length = {17},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5886,
author = {David M. Cerna},
title = {{The Castle Game}},
language = {english},
abstract = {A description of a game for teaching certain aspects of first-order logic based on the Drink's Paradox. },
year = {2019},
length = {3},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5887,
author = {David M. Cerna},
title = {{Manual for AXolotl}},
language = {english},
abstract = {In this document we outline how to play our preliminary version of \textbf{AX}olotl. We present a sequence of graphics illustrating the step by step process of playing the game. },
year = {2019},
length = {9},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5918,
author = {David M. Cerna and Temur Kutsia},
title = {{Higher-Order Pattern Generalization Modulo Equational Theories with a unit element}},
language = {english},
abstract = {We consider anti-unification for simply typed lambda terms in theories defined by associativity,commutativity, identity (unit element) axioms and their combinations, and develop a sound andcomplete algorithm which takes two lambda terms and computes their equational generalizations inthe form of higher-order patterns. The problem is finitary: the minimal complete set of suchgeneralizations contains finitely many elements. We define the notion of optimal solution andinvestigate special fragments of the problem for which the optimal solution can be computed in linearor polynomial time.},
year = {2019},
length = {25},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5936,
author = {David Cerna},
title = {{AXolotl: A Self-study Tool for First-order Logic}},
language = {english},
year = {2019},
month = {May},
length = {4},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5981,
author = {David M. Cerna},
title = {{On the Complexity of Unsatisfiable Primitive Recursively defined $\Sigma_1$-Sentences}},
language = {english},
abstract = {We introduce a measure of complexity based on formula occurrence within instance proofs of an inductive statement. Our measure is closely related to {\em Herbrand Sequent length}, but instead of capturing the number of necessary term instantiations, it captures the finite representational difficulty of a recursive sequence of proofs. We restrict ourselves to a class of unsatisfiable primitive recursively defined negation normal form first-order sentences, referred to as {\em abstract sentences}, which capture many problems of interest; for example, variants of the {\em infinitary pigeonhole principle}. This class of sentences has been particularly useful for inductive formal proof analysis and proof transformation. Together our complexity measure and abstract sentences allow use to capture a notion of {\em tractability} for state-of-the-art approaches to inductive theorem proving, in particular {\em loop discovery} and {\em tree grammar} based inductive theorem provers. We provide a complexity analysis of an important abstract sentence, and discuss the analysis of a few related sentences, based on the infinitary pigeonhole principle which we conjecture represent the upper limits of tractability and foundation of intractability with respect to the current approaches.},
year = {2019},
length = {17},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5991,
author = {David M. Cerna and Rafael Kiesel and Alexandra Dzhiganskaya},
title = {{A Mobile Application for Self-Guided Study of Formal Reasoning}},
language = {english},
abstract = {In this work we introduce AXolotl, a self-study aid designed to guide students through the basics offormal reasoning and term manipulation. Unlike most of the existing study aids for formal reasoning,AXolotl is an Android-based application with a simple touch-based interface. Part of the design goalwas to minimize the possibility of user errors which distract from the learning process. Such as typosor inconsistent application of the provided rules. The system includes a zoomable proof viewer whichdisplays the progress made so far and allows for storage of the completed proofs as a JPEG or L A TEXfile. The software is available on the google play store and comes with a small library of problems.Additional problems may be opened in AXolotl using a simple input language. Currently, AXolotlsupports problems which can be solved using rules which transform a single expression into a set ofexpressions. This covers educational scenarios found in our first semester introduction to logic courseand helps bridge the gap between propositional and first-order reasoning. Future developments willinclude rewrite rules which take a set of expressions and return a set of expressions, as well as aquantified first-order extension.},
year = {2019},
month = {October},
length = {18},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}