With this article, the two authors would like to pay tribute to the memory of their dear friend and colleague Stefen Hölldobler, who left us far too early in 2023. Ulrich (UF), in his time as a postdoc at the University of the Bundeswehr Munich, mentored Stefen as a student in his first logic lectures. Meghna (MB) is Stefen's last PhD student. Although there is so much more to the wonderful man Stefen was, this article strives to briefly touch upon some of the various hats he donned during his lifetime - as a student, a researcher, a professor and a friend. After pursuing a Diploma in Computer Science, Stefen happened to quit the Army and start as a research and Figure 2: Equational Logic Programming. Example taken teaching assistant at the University of the Bundeswehr from [2]. Munich with Prof. Niegel, where UF was working as a postdoc. During his time as a PhD student Stefen started as a visiting research associate at Alan Robinson's Logic Programming Research Group at the Syracuse University, For his PhD-Thesis Stefen concentrated on Equational USA in 1983. During this visit he became interested in Logic Programming and his Dissertation was published the combination of logic and functional programming - in the prestigious Springer series Lecture Notes in AI a topic that paved the way for a very fruitful collabora- [2]. Figure 2 shows an example from his thesis. It is tion between UF and Stefen (e.g. [ 1]). Figure 1 shows an a logic program which contains Horn clauses together example: there is a logic program PYTHAGORAS which with Horn equality theories and has to be evaluated by uses a function * for multiplication. During execution of EP-resolution based on EP-unification. the program it might happen that the arguments of the function are not yet instantiated, such that the function 2. The Postdoc cannot be evaluated; in such a case the unification algorithm uses an equivalent logic program, in our example In 1988 Stefen joined Wolgang Bibel's Intellectics Group the clauses for MULT, to further evaluate the function at TU Darmstadt in Germany and shortly thereafter, in call. 1989, he was ofered a one-year fellowship as a postdoc Stefen and UF published together on this topic and at the International Computer Science Institute (ICSI) at because they were reasonably successful, both were able Berkeley, USA. During this period he still remained true to take a lot of liberties - they were kind of enfants terri- to his theme of equational logic programming. There he ble and enjoyed rebelling against the rigidity of academic was introduced to connectionism by Jerry Feldman and administration. he immediately realised that this method could be used excellently for calculating unifiers. Stefen managed to ifnd a clever representation of terms and the unification problem in order to eficiently use networks for computation. Figure 3 shows an example of the representation
surface , denoted by putdown(v ). Figure 4 shows the
definition of the putdown-operator. If there is a plan or a
sequence of actions whose execution leads to a situation
where the robot is holding a block , then we execute
Figure 3: Computing a Unifier by a Neural Network. Example a plan involving the action putdown, which results in
taken from [3]. the block being on the table with its top clear and the
robot’s hands empty. Analogously, ∘ () ∘ () ∘ is
a term representing a situation where () denotes that
approach could be regarded as cognitively motivated the block is on the table , () denotes that the top of
or whether it was just a clever ’hardware trick’. Any- is clear, and denotes that the robot’s hands are empty.
how, this research at the ICSI finally led to a postdoc- And : putdown() is a term denoting a plan with
toral thesis (Habilitation) on Automated Inferencing and the additional action of putting down.
Connectionist Models in 1993. Stefen received this aca- This approach was further developed by Stefen and
demic degree from TU Darmstadt with Wolfgang Bibel other members of the Darmstadt Intellectics Group
and Larry Feldman as supervisors. Later on in a series [
ifcation theory can be traced in his work on planning — 3. The European Master’s Program shortly after joining Wolfgang Bibel’s Intellectics group in Computational Logic in 1988 Stefen came across various planning approaches.
Together with Josef Schneeberger, he developed a new Stefen became a Professor for Knowledge Representation calculus for deductive planning [5]. The basis for this and Reasoning in the Computer Science Department at approach are equational logic programs [2], where situa- the Technische Universität Dresden in 1993. In 1997 he tions, which depict states of the world, and plans, which established the “International Master’s programme in are sequences of actions that transform one situation Computational Logic (MCL)", which was one of the first to another, are represented by terms. Reasoning about English-language Master’s programmes at a computer situations and plans are performed at the object level science faculty in Germany and thus garnered a lot of and a generated plan precisely corresponds to the well- attention for computer science at TU Dresden. known concept of a computed answer substitution via The “European Master’s Program in Computational SLDE-resolution [6, 2]. Logic", established under his leadership in 2004, expanded
As a small example let us consider a situation, where the previous programme concept [15]. Besides Dresden a robot is holding a block , denoted by ℎ(), and it is re- as a coordinating university the following partners parquired to perform the action of putting down on a table ticipated: Free University of Bozen-Bolzano, Italy, Universidade Nova de Lisboa, Portugal, Technische Univer- tations with respect to the logic programs through the sität Wien, Austria and NICTA, Australia. In 2003, Stef- connectionist networks until they converged to stable fen founded the International Center for Computational states — which were the least models of the programs. Logic (ICCL) as an international competence centre for After his talk Stefen apprehensively asked the audience research and teaching in the field of computational logic. whether these aforementioned stable states have someHe was also committed to the faculty as Dean of Studies thing in common with mental models. Researcher Michiel for international degree programmes. He was the coordi- van Lambalgen, who was in the audience, raised his arm nator of both programmes until 2019 and raised a large and answered: these are mental models. number of Erasmus scholarships. In the period between How humans reason has been a long standing ques2010 and 2014, the two programmes were supplemented tion in psychology and cognitive science, with many by the DAAD-funded “International PhD Program in paradigms attempting to explain and put together pieces Computational Logic" through his initiative. of the extraordinary puzzle. Following psychologist
Stefen organised numerous international summer Philip Johnson Laird in [17], Stefen too began considschools for students both at TU Dresden and in Viet- ering the question, “are there general ways of thinking nam, Indonesia, Thailand and Mongolia, among others. that humans follow when they make deductions?". Given These Asian summer schools lasted 2 weeks each, dur- Stefen’s background in mathematics and computational ing which a group of German colleagues taught students. logic, his preliminary attempt was to consider classical During this time Stefen’s many talents became appar- two-valued logic. After all it has been considered a norent. Organisation in an Asian country was certainly not mative theory for many accounts of human reasoning. always easy but Stefen managed to organise everything However, as many studies have hence indicated, it is with remarkable ease. Not only did he enjoy organis- perhaps safe to say that classical two-valued logic is no ing the course, but he was also enthusiastic to teach longer considered as the doctrine for the same [18]. To and got the participants excited about Computational that end, Stefen and his colleagues began exploring the Logic. Whenever possible, the lecturers also attended three-valued non-monotonic logic paradigm and thus bethe courses of their colleagues and this helped develop a gan the development of the Weak Completion Semantics. special relationship among them during the time spent Stefen’s broad long term research goal was to develop at the summer schools. The many weeks UF was able a computational and comprehensive (cognitive) theory to spend during these occasions are certainly among his for adequately modelling human reasoning tasks. He fondest memories. envisioned the theory to be computational such that hu
During the Mongolian summer school MB accompa- man responses to a reasoning task may be computed, nied the team as a student assistant. At that time she was and comprehensive such that the theory may be able to pursuing a master’s degree in Computational Logic at encompass a wide variety of tasks. The Weak CompleTU Dresden and met Stefen through his formidable logic tion Semantics is based on ideas initially proposed by lectures. The trip to Mongolia left a lasting impression Keith Stenning and Michiel van Lambalgen in [19]. It is in MB’s mind and she looks back at them with immense mathematically sound [20], has been applied to various fondness and gratitude to this day. Stefen had been her human reasoning tasks such as the suppression task [21], friend, philosopher and guide ever since and played a the selection task [22], the belief-bias efect [ 23], ethical very important role in her life. decision-making [24] etc. It has outperformed the twelve cognitive theories considered by Philip Johnson-Laird and Sangeet Khemlani [25] in syllogistic reasoning [26] 4. Cognitive Science and Logic and is implementable in a connectionist setting [27].
tact with Cognitive Science through his involvement with Connectionism. Also the discussions in the Darmstadt Intellectics group about Johnson Laird’s work on deduction, after the publication of [16], made him familiar with the subject area.
However, he finally stumbled into the field of Cognitive Science in the year 2007, when he presented an idea of computing semantic operators associated with logic programs by feed-forward connectionist networks at a lecture in the summer school of the International Center of Computational Logic at TU Dresden. He put forward the proposal of recursively propagating (logical) interpre
As a brief demonstrative example of how the Weak Completion Semantics (WCS) can be used to model human reasoning scenarios, let us consider an excerpt from an experiment, dubbed as the suppression task, which was conducted by psychologist Ruth Byrne [28] following [29, 30, 31], in order to study if and under what circumstances humans suppress classically valid responses such as modus ponens and modus tollens.
Let us begin with the given premises, if she has an essay to write, then she will study late in the library and she has an essay to write. For any reasoning episode the first step within the WCS framework is to construct a representative logic program. In line with the above premises we thus construct the following program, : { ← ∧ ¬ab, ab ← ⊥ , ← ⊤} , where and represent that she has an essay to write and that she will study late in the library, respectively. The abnormality predicate ab is assumed to be false. The abnormality predicate serves the purpose of the (default) assumption that nothing is abnormal with regards to a given context — something humans seem to assume when reasoning with limited information, as was suggested in [19]. Weakly completing results in ( ): { ↔ ∧ ¬ab, ab ↔ ⊥, ↔ ⊤}, whose least model (the step by step computation of which is excluded from the current discussion for simplification purposes) is ⟨{, }, {ab}⟩. Here, the atoms and are true while ab is false. Anything outside the scope of this model is unknown in this context. In other words, the reasoner concludes that she will study late in the library, which forms the majority consensus in the experiments reported by Byrne.
Now, if the above premises were to be supplemented with an additional premise: if the library stays open, then she will study late in the library, the set would be represented by the following program ′: { ← ← ∧ ¬ab, ab ← ⊥ ∧ ¬ab, ab ← ⊥ , , ab ← ¬ , ab ← ¬
, ← ⊤} , where the meanings of the previously mentioned atoms remain the same, denotes the library stays open and ab denotes any abnormality with respect to the library staying open. The two definitions of ab semantically mean that either there is nothing abnormal with respect to having an essay to write (the default assumption) or as suggested by the addition of the above premise, there may be something abnormal namely that the library might be closed. Similarly the definitions of ab semantically mean that either there is no abnormality with regards to the library staying open or there is no essay to write.
Now, weakly completing ′ results in ( ′): { ↔ ( ∧ ¬ab) ∨ ( ∧ ¬ab), ab ↔ ⊥ ∨ ¬, ab ↔ ⊥ ∨ ¬,
↔ ⊤}, whose least model is ⟨{}, {ab}⟩, where is true and ab is false. As is unknown with respect to this model, 2–7 the previously drawn conclusion, she will study late in the library, is now suppressed and the reasoner concludes that she may or may not study late in the library. This phenomenon is the so-called suppression efect reflected in the experiments reported by Byrne. In the demonstrated case, even when the antecedent is afirmed i.e. a person has an essay to write, reasoners may not automatically conclude that the person will study late in the library (i.e. draw an MP conclusion) because there is a possibility of the library being closed which may disable the person from doing so. Analogously in the context of the least model of ( ′), it is unknown whether the library stays open () or not hence the atom ab is unknown. And this means is (also) unknown in the least model.
four monographs, more than 100 scientific articles and edited more than 30 publications. Aside his own research, Stefen had moreover been very active in his academic community, organising workshops and conferences and serving for many years on the selection committee for the GI Doctoral Award. He also held a honorary professorship from Stavropol university, but at the same time was horrified by the recent Russian war of aggression in Ukraine. One of his last activities before he fell ill was the attempt to organise a scientific event in parallel to the 17th annual G20 summit in November 2022 in Bali in order to demonstrate peaceful and friendly coexistence among scientists across all borders.
In this article the authors have tried to focus on the various aspects of Stefen’s work. However, the limited scope of this article does not and cannot assimilate the essence of the man Stefen was. And this commemoration would indeed be incomplete without emphasising that while a good scientist, Stefen was also a people person — his presence in a room could hardly go unnoticed. He was a family man and a loving father. As MB fondly recollects, he would often advise her to not stress about “small" things and reminded her time and again that happiness is the most important thing in life. As he would often say, das Leben ist schön — life is beautiful.
Indeed, the authors will terribly miss their dear friend and bid him a very fond farewell.