Steffen Hölldobler

• Dr.rer.nat.habil.
• Professor (Full) at TU Dresden

In their book, Noise: A Flaw in Human Judgment, the authors Daniel Kanheman, Olivier Sibony andCass R. Sunstein highlight the importance of minimizing bias, i.e. systematic deviation, and noise, i.e.variability, in judgments in order to reduce error. Bias has long been the subject of many discussions butnoise is yet to gain the attention it deserve...

Modus tollens is a rule of inference in classical, two-valued logic which allows to derive the negation of the antecedent from a conditional and the negation of its consequent. In this paper, we investigate when humans draw such conclusions and what modulates the application of modus tollens. We consider conditionals which may or may not be obligat...

Numerous results in psychology demonstrate that inferences humans draw from conditional sentences (i.e., sentences of the form "if antecedent then consequent") differ systematically from classical two-valued logical inferences. Today , still no formal approach yet exists which captures the specifics of semantic differences between types of conditio...

The weak completion semantics is a three-valued, non-monotonic theory which has been shown to adequately model various cognitive reasoning tasks. In this paper we extend the weak completion semantics to model disjunctions and exclusive disjunctions. Such disjunctions are encoded by integrity constraints and skeptical abduction is applied to compute...

An experiment has revealed that if the antecedent of a conditional sentence is denied, then most participants conclude that the negation of the consequent holds. However, a significant number of participants answered nothing follows if the antecedent of the conditional sentence was non-necessary. The weak completion semantics correctly models the a...

The weak completion semantics is a novel cognitive theory. It is multi-valued, non-monotonic, and knowledge-rich, allows learning, can handle inconsistent background knowledge, and can be applied to model the average reasoner. Moreover, it uses abduction to explain observations, to satisfy integrity constraints, and to search for counterexamples. I...

Psychological experiments have shown that humans do not reason according to classical logic. Therefore, we might argue that logic-based approaches in general are not suitable for modeling human reasoning. Yet, we take a different view and are convinced that logic can help us as an underlying formalization of a cognitive theory, but claim rather tha...

The Weak Completion Semantics is a computational and nonmonotonic cognitive theory based on the three-valued logic of Lukasiewicz. It has been applied to adequately model -- among others -- the suppression task, the selection task, syllogistic reasoning, and conditional reasoning. In this paper we investigate the case where the antecedent of a cond...

The Weak Completion Semantics is a computational and nonmonotonic cognitive theory based on the three-valued logic of Łukasiewicz. It has been applied to adequately model – among others – the suppression task, the selection task, syllogistic reasoning, and conditional reasoning. In this paper we investigate the case where the antecedent of a condit...

The Weak Completion Semantics is a novel cognitive theory which has been successfully applied -- among others -- to the suppression task, the selection task and syllogistic reasoning. It is based on logic programming with skeptical abduction. Each weakly completed program admits a least model under the three-valued Lukasiewicz logic which can be co...

The adjective cognitive especially in conjunction with the word computing seems to be a trendy buzzword in the artificial intelligence community and beyond nowadays. However, the term is often used without explicit definition. Therefore we start with a brief review of the notion and define what we mean by cognitive reasoning. It shall refer to mode...

The Weak Completion Semantics is a novel, integrated and computational cognitive theory. Recently, it has been applied to ethical decision making. To this end, it was extended by equational theories as needed by the fluent calculus. To compute least models equational matching problems have to be solved. Do humans consider equational matching in rea...

The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs, three-valued Lukasiewicz logic, weak completion , and skeptical abduction. It has been successfully applied-among others-to the suppression task, the selection task, and to human syllogistic reasoning. In order to solve ethical...

The weak completion semantics is a novel computational theory based on logic programs. It is extended to deal with equalities, which is a prerequisite to represent and reason about actions and causality as in the fluent calculus. This is discussed in the context of ethical decision making. In order to decide questions about the moral permissi-bilit...

The Weak Completion Semantics is a novel cognitive theory which has been successfully applied to the suppression task, the selection task, syllogistic reasoning, the belief bias effect, spatial reasoning as well as reasoning with conditionals. It is based on logic programming with skeptical abduction. Each program admits a least model under the thr...

It seems widely accepted that human reasoning cannot be modeled by means of classical logic. Psychological experiments have repeatedly shown that participants’ answers systematically deviate from the classical logically correct answers. Recently, a new computational logic approach to modeling human syllogistic reasoning has been developed which see...

A recent meta-analysis~\cite{Khemlani2012} showed that the conclusions drawn by humans in psychological experiments about syllogistic reasoning deviate from the conclusions drawn by classical logic. Moreover, none of the current cognitive theories predictions fit the empirical data. In this paper we show how human syllogistic reasoning can be model...

In everyday life, it seems that we prefer some explanations for an observation over others because of our contextual background knowledge. Reiter already tried to specify a mechanism within logic that allows us to avoid explicitly considering all exceptions in order to derive a conclusion w.r.t. the usual case. In a recent paper, a contextual reaso...

We present a new logic programming approach to contextual reasoning, based on the Weak Completion Semantics (WCS), the latter of which has been successfully applied in the past to adequately model various human reasoning tasks. One of the properties of WCS is the open world assumption with respect to undefined atoms. This is a characteristic that i...

The game of Go is known to be one of the most complicated board games. Competing in Go against a professional human player has been a long-standing challenge for AI. In this paper we shed light on the AlphaGo program that could beat a Go world champion, which was previously considered non-achievable for the state of the art AI.

Conditionals play a prominent role in human reasoning and, hence, all cog-nitive theories try to evaluate conditionals like humans do. In this paper, we are particularly interested in the Weak Completion Semantics, a new cognitive theory based on logic programming, the weak completion of a program, the three-valued Łukasiewicz logic, and abduction....

Various real-world problems can be formulated as the task of counting the models of a propositional formula. This problem, also called #SAT, is therefore of practical relevance. We present a formal framework describing a novel approach based on considering the formula in question together with its negation. This method enables us to close search br...

A recent meta-analysis [KJ12] showed that the conclusions drawn by humans in psychological experiments about syllogistic reasoning deviate from the conclusions drawn by classical logic. Moreover, none of the current cognitive theories predictions fit the empirical data. In this paper an analysis by computational logics clarifies seven principles ne...

In everyday life, it seems that when we observe something, then, while searching for explanations, we assume some explanation more plausible to others, simply because of our contextual background. Recently, a contextual reasoning approach has been presented, which takes into account this contex-tual background and allows us to specify context withi...

In a recent meta-analysis, Khemlani & Johnson-Laird (2012) showed that the conclusions drawn by human reasoners in psychological experiments about syllogistic reasoning are not the conclusions predicted by classical �rst-order logic. Moreover, current cognitive theories deviate signi�cantly from the empirical data. In this paper we show how human s...

There is an ongoing debate in the psychology of reasoning whether and how logic can be used to describe the human inference process. Many psychological findings indicate that humans deviate from classical logic inferences. Some researchers have proposed to use ternary logics instead to model human reasoning processes. In this article we re-analyze...

We present a new approach to evaluate conditionals in human reasoning. This approach is based on the weak completion semantics which has been successfully applied to adequately model various other human reasoning tasks in the past. The main idea is to explicitly consider the case, where the condition of a conditional is unknown with respect to some...

I present a logic programming approach based on the weak completions semantics to model human reasoning tasks, and apply the approach to model the suppression task, the selection task as well as the belief-bias effect, to compute preferred mental models of spatial reasoning tasks and to evaluate indicative as well as counterfactual conditionals.

We present a new connectionist network to compute skeptical abduction. Combined with the CORE method to compute least fixed points of semantic operators for logic programs, the network is a pre-requisite to solve human reasoning tasks like the suppression task in a connectionist setting.

In this paper we present a new approach to evaluate indicative conditionals with respect to some background information specified by a logic program. Because the weak completion of a logic program admits a least model under the three-valued Lukasiewicz semantics and this semantics has been successfully applied to other human reasoning tasks, condit...

Formal approaches that aim at representing human reasoning should be evaluated based on how humans actually reason. One way of doing so is to investigate whether psychological findings of human reasoning patterns are represented in the theoretical model. The computational logic approach discussed here is the so-called weak completion semantics whic...

Modern propositional satisfiability (or SAT) solvers are very powerful due to recent developments on the underlying data structures, the used heuristics to guide the search, the deduction techniques to infer knowledge, and the formula simplification techniques that are used during pre- and inprocessing. However, when all these techniques are put to...

Solving Constraint Satisfaction Problems (CSPs) by Boolean Satisfiability (SAT) requires suitable encodings for translating CSPs to equivalent SAT instances that should not only be effectively generated, but should also be efficiently processed by SAT solvers. In this paper we investigate hierarchical and hybrid encodings, focussing on two specific...

The belief bias effect is a phenomenon which occurs when we think that we judge an argument based on our reasoning, but are actually influenced by our beliefs and prior knowledge. Evans, Barston and Pollard carried out a psychological syllogistic reasoning task to prove this effect. Participants were asked whether they would accept or reject a give...

In this paper we discuss conjunctive planning problems in the context of the fluent calculus and Petri nets. We show that both formalisms are equivalent in solving these problems. Thereafter, we extend actions to contain preconditions as well as obstacles. This requires to extend the fluent calculus as well as Petri nets. Again, we show that both e...

Modern propositional satisfiability (or SAT) solvers are very powerful due to recent developments on the underlying data structures, the used heuristics to guide the search, the deduction techniques to in- fer knowledge, and the formula simplification techniques that are used during pre- and inprocessing. However, when all these techniques are put...

We provide a tutorial on answer set programming, a modern approach towards true declarative programming. We first introduce the required theoretical background in a compact, yet sufficient way and continue to elaborate problem encodings for some well known problems. We do so by also introducing the tools gringo and clasp, a sophisticated state-of-t...

Many different encodings for pseudo-Boolean constraints into the Boolean satisfiability problem have been proposed in the past. In this work we present a novel small sized and simple to implement encoding. The encoding maintains generalized arc consistency by unit propagation and results in a formula in conjunctive normal form that is linear in siz...

In this paper, periodic event scheduling problems (PESP) are encoded as satisfiability problems (SAT) and solved by a state-of-the-art SAT solver. Two encodings, based on direct and order encoded domains, are presented. An experimental evaluation suggests that the SAT-based approach using order encoding outperforms constraint-based PESP solvers, wh...

In this paper we contribute to bridging the gap between human reasoning as studied in Cognitive Science and commonsense reasoning based on formal logics and formal theories. In particular, the suppression task studied in Cognitive Science provides an interesting challenge problem for human reasoning based on logic. The work presented in the paper i...

This paper surveys modern parallel SAT-solvers. It focusses on recent successful techniques and points out weaknesses that have to be overcome to exploit the full power of modern multi-core processors.

The paper discusses cache utilization in state-of-the-art SAT solvers. The aim of the study is to show how a resource-unaware SAT solver can be improved by utilizing the cache sensibly. The analysis is performed on a CDCL-based SAT solver using a subset of the industrial SAT Competition 2009 benchmark. For the analysis, the total cycles, the resour...

To understand and to model human reasoning is a goal that was established already by the Greek philosopher Aristotle. With computers becoming more and more part of our daily life and the increased effort to mechanize thought processes, this goal becomes even more important. Until recently, a large part of the Cognitive Science community was convinc...

We propose to model human reasoning tasks using completed logic programs interpreted under the three-valued Lukasiewicz semantics. Given an appropriate immediate consequence operator, completed logic programs admit a least model, which can be computed by iterating the consequence operator. Reasoning is then performed with respect to the least model...

If logic programs are interpreted over a three-valued logic, then often Kleene’s strong three-valued logic with complete equivalence and Fitting’s associated immediate consequence operator is used. However, in such a logic the least fixed point of the Fitting operator is not necessarily a model for the program under consideration. Moreover, the mod...

Knowledge-based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structure-sensitive processes as expressed e.g., by means of first-order predicate logic, it is not obvious at all what neural-symbolic...

We report on an experiment where we inserted symbolic rules into a neural network during the training process. This was done to guide the learning and to help escape local minima. The rules are constructed by analysing the errors made by the network after training. This process can be repeated, which allows to improve the network performance again...

Research into the processing of symbolic knowledge by means of connectionist networks aims at systems which combine the declarative nature of logicbased artificial intelligence with the robustness and trainability of artificial neural networks. This endeavour has been addressed quite successfully in the past for propositional knowledge representati...

The well-founded semantics (WFS) for logic programs is one of the few major paradigms for closed-world reasoning. With the advent of the Semantic Web, it is being used as part of rule systems for ontology reasoning, and also investigated as to its usefulness as a semantics for hybrid systems featuring combined open- and closed-world reasoning. Even...

We present a fully connectionist system for the learning of first-order logic programs and the generation of corresponding models: Given a program and a set of training examples, we embed the associated semantic operator into a feed-forward network and train the network using the examples. This results in the learning of first-order knowledge while...

In this paper, we present a new decompositional approach for the extraction of propositional rules from feed-forward neural networks of binary threshold units. After decomposing the network into single units, we show how to extract rules describing a unit's behavior. This is done using a suitable search tree which allows the pruning of the search s...

Part-of-speech tagging (POS) assigns grammatical tags (like noun, verb, etc.) to a word depending on its definition and its context. This is a first step before parsing may be applied. POS tagging and more generically word tagging, plays an important role in computational linguistics and in many information retrieval and text mining tasks. Neither...

We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then p...

Knowledge based artificial networks networks have been ap- plied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to struc- tured objects and structure-sensitive processes it is not obvious at all how neural symbolic systems should look like such that they are truly conne...

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way tha...

We present the fuzzy linguistic description logic ALC_FL, an instance of the description logic framework ALC with the certainty lattice characterized by a hedge algebra. Beside constructors of ALC, ALC_FL allows the modiflcation by hedges.

We present a new approach for solving first-order Markov decision processes combining first-order state abstraction and heuristic search. In contrast to existing systems, which start with propositionalizing the decision process and then perform state abstraction on its propositionalized version we apply state abstraction directly on the decision pr...

In this paper, we present the fuzzy description logic ALCFLH. ALCFLH is based on ALCFH, but linear hedges are used instead of exponential ones. This allows to solve the entailment and the subsumption problem in a fuzzy description logic, where arbitrary concepts and roles may be modified.

We present a first-order value iteration algorithm that ad-dresses the scalability problem of classical dynamic program-ming techniques by logically partitioning the state space. An MDP is represented in the Probabilistic Fluent Calculus, that is a first-order language for reasoning about actions. More-over, we develop a normalization algorithm tha...

In their seminal paper (1) McCulloch and Pitts have shown the strong relationship between nite automata and so-called McCulloch- Pitts networks. Our goal is to extend this result to weighted automata. In other words, we want to integrate articial neural networks and weighted automata. For this task, we introduce semiring articial neural networks, t...

One facet of the question of integration of Logic and Connectionist Systems, and how these can complement each other, concerns the points of contact, in terms of semantics, between neural networks and logic programs. In this paper, we show that certain semantic operators for propositional logic programs can be computed by feedforward connectionist...

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way tha...