Automated Reasoning

@techreport{RISC7056,
author = {G. Ehling and T. Kutsia},
title = {{Solving Quantitative Equations}},
language = {english},
abstract = {Quantitative equational reasoning provides a framework that extends equality to an abstract notion of proximity by endowing equations with an element of a quantale. In this paper, we discuss the unification problem for a special class of shallow subterm-collapse-free quantitative equational theories. We outline rule-based algorithms for solving such equational unification problems over generic as well as idempotent Lawvereian quantales and study their properties.},
number = {24-03},
year = {2024},
month = {April},
keywords = {quantitative equational reasoning, Lawvereian quantales, equational unification},
length = {23},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC7084,
author = {W. Windsteiger},
title = {{Gray-Box Proving in Theorema}},
language = {english},
abstract = {Many theorems in mathematics have the form of an implication, an equivalence, or an equality, and in the standard prover in the Theorema system such formulas are handled by rewriting. Definitions ofnew function- or predicate symbols are yet another example of formulas that require rewriting in their treatment inthe Theorema system. Both theorems and definitions in practice often carry conditions under which they are valid. Rewriting is, thus, only valid in cases where all side-conditions are met. On the other hand, many of these side-conditions are trivial and when presenting a proof we do not want to distract the reader with lengthy derivations that justify the side-conditions. The goal of this paper is to present the design and implementation of a mechanism that efficiently checks side-conditionsin rewriting while preserving the readability and the explanatory power of a mathematical proof, which has always been of centralinterest in the development of the Theorema system.},
number = {24-07},
year = {2024},
month = {July},
keywords = {Theorema, Automated Theorem Proving, Conditional Rewriting, Mathematica},
length = {8},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

@techreport{RISC6684,
author = {Bruno Buchberger},
title = {{Is ChatGPT Smarter Than Master’s Applicants?}},
language = {English},
abstract = {During the selection procedure for a particular informatics fellowship program sponsored by Upper Austrian companies, I ask the applicants a couple of simple technical questions about programming, etc., in a Zoom meeting. I put the same questions to the dialogue system ChatGPT, [ChatGPT]. The result surprised me: Nearly all answers of ChatGPT were totally correct and nicely explained. Also, in the dialogues to clarify some critical points in the answers, the explanations by ChatGPT were amazingly clear and goal-oriented.In comparison: I tried out the same questions in the personal Zoom interviews with approximately 30 applicants from five countries. Only the top three candidates (with a GPA of 1.0, i.e., the highest possible GPA in their bachelor’s study) performed approximately equally well in the interview. All the others performed (far) worse than ChatGPT. And, of course, all answers from ChatGPT came within 1 to 10 seconds, whereas most of the human applicants' answers needed lengthy and arduous dialogues.I am particularly impressed by the ability of ChatGPT to extract meaningful and well-structured programs from problem specifications in natural language. In this experiment, I also added some questions that ask for proofs for simple statements in natural language, which I do not ask in the student's interviews. The performance of ChatGPT was quite impressive as far as formalization and propositional logic are concerned. In examples where predicate logic reasoning is necessary, the ChatGPT answers are not (yet?) perfect. I am pleased to see that ChatGPT tries to present the proofs in a “natural style” This is something that I had as one of my main goals when I initiated the Theorema project in 1995. I think we already achieved this in the early stage of Theorema, and we performed this slightly better and more systematically than ChatGPT does.I also tried to develop a natural language input facility for Theorema in 2017, i.e., a tool to formalize natural language statements in predicate logic. However, I could not continue this research for a couple of reasons. Now I see that ChatGPT achieved this goal. Thus, I think that the following combination of methods could result in a significant leap forward:- the “natural style” proving methods that we developed within Theorema (for the automated generation of programs from specifications, the automated verification of programs in the frame of knowledge, and the automated proof of theorems in theories), in particular, my “Lazy Thinking Method” for algorithm synthesis from specifications- and the natural language formalization techniques of ChatGPT.I propose this as a research project topic and invite colleagues and students to contact me and join me in this effort: Buchberger.bruno@gmail.com.},
number = {23-04},
year = {2023},
month = {January},
keywords = {ChatGPT, automated programming, program synthesis, automated proving, formalization of natural language, master's screening},
length = {30},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}