A Brief Introduction Into Activation-Based Conditional Inference Marco Wilhelm 1[0000-0003-0266-2334] , Diana Howey 1[0000-0002-7203-4862] , Gabriele Kern-Isberner 1[0000-0001-8689-5391] , Kai Sauerwald 2[0000-0002-1551-7016] , and Christoph Beierle 2[0000-0002-0736-8516] 1 Dept. of Computer Science, TU Dortmund University, Dortmund, Germany {marco.wilhelm, diana.howey, gabriele.kern-isberner}@cs.tu-dortmund.de 2 Dept. of Computer Science, FernUniversit¨ at in Hagen, Hagen, Germany {kai.sauerwald, christoph.beierle}@fernuni-hagen.de Abstract. Activation-based conditional inference integrates several as- pects of human reasoning into formal conditional reasoning, such as fo- cusing, forgetting, and remembering, by combining conditional reasoning and the cognitive architecture ACT-R. The idea is to select a reasonable subset of a conditional belief base before drawing inferences. The selec- tion is based on an activation function which assigns to the conditionals in the belief base a degree of activation based on the conditional’s rele- vance for the current query and its usage history. 1 Introduction Activation-based conditional inference combines ACT-R [2, 1] and conditional reasoning. ACT-R (Adaptive Control of Thought-Rational ) is a well-founded cog- nitive architecture developed to formalize human reasoning in which a selection of cognitive entities (chunks as declarative memory and production rules as pro- cedural memory) is performed before these entities are used to solve a reasoning task. From a cognitive point of view, there are basically two processes which af- fect the selection: The long-term process of forgetting and remembering and the short-term process of activating certain beliefs depending on the current context. In this paper, we adapt the concept of (de)activation of cognitive entities from ACT-R and combine it with the task of drawing conditional inferences. More precisely, we define an activation function for conditionals of the form (B|A) with the meaning “if A holds, then usually B holds, too.” The conditionals with the highest activation are selected for the inference task. Therewith, we general- ize the concept of focused inference [6] and give it a profound cognitive meaning, and we also equip ACT-R with a modern, high quality inference formalism. 2 Logical Foundations We consider a propositional language L over a finite set of atoms Σ which we ex- tend to the conditional language (L|L)= {(B|A) | A, B ∈ L} where conditionals Proceedings of the 7th Workshop on Formal and Cognitive Reasoning Copyright c  2021 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). 4