Can Formal Non-monotonic Systems Properly Describe Human Reasoning?
Gregory Kuhnmünch, Marco Ragni · Cognitive Science · 2014
Can Formal Non-monotonic Systems Properly Describe Human Reasoning? Gregory Kuhnmunch ([email protected]) Department of cognitive Science, Friedrichstrase 50, 79098 Freiburg, Germany Marco Ragni ([email protected]) Department of cognitive Science, Friedrichstrase 50, 79098 Freiburg, Germany Abstract Monotonic (logical) reasoning makes the strong claim that an inference cannot be contradicted by future information; an assumption contrary to everyday life experience. This assumption is relaxed in non-monotonic reasoning. However, there are only few formal non-monotonic theories of reasoning that have inspired psychological theory-building. Can formal systems such as cumulative logic (system C) or preferential logic (system P), developed in philosophy and artificial intelligence, predict human non-monotonic inferences? Previous investigations have mainly used probabilistic representations of these systems and it remains unclear whether participants make the same inferences based on a qualitative description. We describe a different methodological approach and report related experimental findings that run counter to current approaches to human non- monotonic reasoning. Implications of our proposed method are discussed. Keywords: human rationality; non-monotonic reasoning; belief revision; decision experiment; systems C, CL, and P Introduction Non-monotonic reasoning (NMR) is important for artificial intelligence (AI), but indispensable for everyday human reasoning. When we derive new information, we are often aware of the fact that information acquired later on can contradict previous conclusions or existing knowledge. Therefore, we are forced to resolve the contradiction to an extent that allows us to act efficiently in the world. This holds for rules of deontic reasoning, too: In what circumstances am I allowed to cross a red traffic light? In daily life we have to deal with exceptions from otherwise predominantly valid rules (Do not cross when the traffic light is red). Other domains are naive psychology and theory of mind: Our initial assumptions about another's thoughts, emotions, or motives require revision once we have made new inconsistent observations of that person's behavior. Hence, everyday thinking is often non-monotonic (Pollock, 2008, only abstract available) – it requires NMR and dealing with exceptions. Similarly, expert systems or databases in AI might have to address such problems and therefore, classical designs are augmented by NMR-capabilities. Let us define a logic as non-monotonic if the set of (logical) conclusions from a theory (or knowledge base) is not necessarily preserved when new information is added to the theory. Previous conclusions or premises (declarative knowledge) might be retracted, similarly to belief revision (cp. Kraus, Lehmann & Magidor, 1990). Retraction means that their validity is lost – they are removed because their correctness is not warranted any more. As a central result of psychological research take Byrne's (1989) suppression task: New knowledge about alternatively sufficient or additionally necessary premises can modulate validity of conclusions w.r.t. propositional logic. How could a theory describe human NMR? There are formal (non)- monotonic systems from AI (e.g., Kraus et al., 1990) and psychology (e.g., Pfeifer & Kleiter, 2005) that describe which conclusions can be derived under differing rationality assumptions. In AI, these assumptions are derived from logic; in psychology the standard is typically laymen's performance. Humans deviate from propositional logic (e.g., in the suppression task) and, more generally, conditional reasoning. Nonetheless, there are many other logics and there is a claim according to which non-montonic logics can (substantially) describe these findings (Dietz, Holldobler, & Ragni, 2012; Stenning & van Lambalgen, 2006; 2008). Many other proponents investigate NMR systems: Benferhat, Bonnefon and Da Silva Neves, 2005; Elio and Pelletier (1997); Ford (2004), only to name a few. Table 1: Rules of propositional logic and of systems C, CL, and P. OR and D are only valid in system P; LP is only valid in CL. Refl is reflexivity, SupCl is supraclassicality. System Rules Propositional Logic C (Cumulative) P + MT, CP, TT, EHD CL (Cumul.+Loop) P (Preferential) Extensions of P Refl, LLE, RW, CT, CM; EV; AND, MPC, SupCl C + Loop C + OR, S (= HHD), D (proof by case) DR, RM etc. As we cannot describe the properties of all existing systems, we will focus on (i) three systems relevant for our experiment, that is systems C, CL, and P and (ii) the following rules: Loop (LP), Left Logical Equivalence (LLE), Right Weakening (RW), Cut (CT), Equivalence (EV), AND (AND), Modus Ponens in the Conclusion (MPC), Contraposition (CP), Transitivity (TT), OR (OR), Proof by Case (D), Disjunctive Rationality (DR), Rational