A Variant of Material Connexive Logic

The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius' (and thus, Aristotle's) Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.

Student Development in Logical Reasoning: Results of an Intervention Guiding Students Through Different Modes of Visual and Formal Representation

Due to growing interest in twenty-first-century skills, and critical thinking as a key element, logical reasoning is gaining increasing attention in mathematics curricula in secondary education. In this study, we report on an analysis of video recordings of student discussions in one class of seven students who were taught with a specially designed course in logical reasoning for non-science students (12th graders). During the course of 10 lessons, students worked on a diversity of logical reasoning tasks: both closed tasks where all premises were provided and everyday reasoning tasks with implicit premises. The structure of the course focused on linking different modes of representation (enactive, iconic, and symbolic), based on the model of concreteness fading (Fyfe et al., 2014). Results show that students easily link concrete situations to certain iconic referents, such as formal (letter) symbols, but need more practice for others, such as Venn and Euler diagrams. We also show that the link with the symbolic mode, i.e. an interpretation with more general and abstract models, is not that strong. This might be due to the limited time spent on further practice. However, in the transition from concrete to symbolic via the iconic mode, students may take a step back to a visual representation, which shows that working on such links is useful for all students. Overall, we conclude that the model of concreteness fading can support education in logical reasoning. One recommendation is to devote sufficient time to establishing links between different types of referents and representations.

Argumentation schemes as a way of arguments studies

The paper investigates argument (argumentation) schemes that are used in the theory of argumentation for analyzing everyday reasoning. Such schemes should be understood as structures representing the most general types of argument. Today they are studied not only from theoretical perspectives but also in relation to their application in education and information technologies. Argumentation schemes allow us to identify, produce and evaluate real arguments, as well as critically assess discussions. Despite their popularity, argumentation schemes face some problems. The current presentation introduces the concept of schemes, describes their possible classifications, analyzes strengths and limitations in various approaches. However, the main focus of the paper is on the direction in which the conception of an argument scheme is being developed. I argue that the new stage of its development can be correlated with the birth of a dynamic style of argument in­vestigation that is opposed to a static version. A similar dichotomy can be observed in logic that stands for two types of formality: as pertaining to forms and as pertaining to rules.

Visuospatial Reasoning

Visual thinking has aided many scientific discoveries and is also useful in everyday reasoning. The Animation Tutor provides animation feedback to help students improve their ability to estimate and calculate answers to problems. Examples include calculating the average speed of a round trip and using spatial relationships as a substitute for deriving algebraic solutions. Computer simulations of human thinking have emphasized rule-based reasoning, but these simulations now include a visual buffer to model visuospatial reasoning. It is often difficult to discover new information in visual images such as reinterpreting an ambiguous figure although people are more successful in mentally combining figures to create useful objects. Applications of research on cognitive geography include improving spatial information, geographic education, map design, urban planning, and landscape design.

The logic of uncertainty in law and life

My central interest is decision making in the presence of epistemic uncertainty. A method appropriate for both specialized inquiries and everyday reasoning is based on credal logic, which employs multivalent degrees of belief rather than traditional probability theory. It accounts for epistemic uncertainty as unallocated belief. It holds that, when facing real uncertainty, if a person believes a and believes b, then the person believes a and b together. This brand of multivalent logic underlies and justifies how legal decision makers and the rest of us find facts in a world infused with epistemic uncertainty. Indeed, this article closes by showing the equivalence of multivalent logic and inference to the best explanation. By demonstrating this similarity in reasoning, I aim to shore up our faith in the logic of traditional legal reasoning.

Logical Reasoning in Formal and Everyday Reasoning Tasks

Logical reasoning is of great societal importance and, as stressed by the twenty-first century skills framework, also seen as a key aspect for the development of critical thinking. This study aims at exploring secondary school students’ logical reasoning strategies in formal reasoning and everyday reasoning tasks. With task-based interviews among 4 16- and 17-year-old pre-university students, we explored their reasoning strategies and the reasoning difficulties they encounter. In this article, we present results from linear ordering tasks, tasks with invalid syllogisms and a task with implicit reasoning in a newspaper article. The linear ordering tasks and the tasks with invalid syllogisms are presented formally (with symbols) and non-formally in ordinary language (without symbols). In tasks that were familiar to our students, they used rule-based reasoning strategies and provided correct answers although their initial interpretation differed. In tasks that were unfamiliar to our students, they almost always used informal interpretations and their answers were influenced by their own knowledge. When working on the newspaper article task, the students did not use strong formal schemes, which could have provided a clear overview. At the end of the article, we present a scheme showing which reasoning strategies are used by students in different types of tasks. This scheme might increase teachers’ awareness of the variety in reasoning strategies and can guide classroom discourse during courses on logical reasoning. We suggest that using suitable formalisations and visualisations might structure and improve students’ reasoning as well.

Abductive reasoning: let’s Find Out some models

We present preliminary results on modelling structure of solutions to a task involving abductive reasoning. Research data were gathered using our new tool—Find Out, which has been designed in order to account empirically for abduction relatively close to everyday reasoning processes, with the necessary level of procedure standardization. The tool enables to capture abduction as a compound form of reasoning, from both product and process perspective. Find Out is set up as a game that requires playing the role of an investigator seeking an explanation of what has happened in the presented enigmatic situation. The task consists of three time-limited stages that require different reasoning activities (forming and evaluating of hypotheses, devising final explanations). In the paper, we present quantitative models of structures of solutions to the task proposed by the subjects in the form of situational graphs. We present also some ideas concerning qualitative characteristics of these solutions.

Leaping to conclusions: Why premise relevance affects argument strength

Everyday reasoning requires more evidence than raw data alone can provide. We explore the idea that people can go beyond this data by reasoning about how the data was sampled. This idea is investigated through an examination of premise non‐monotonicity, in which adding premises to a category‐based argument weakens rather than strengthens it. Relevance theories explain this phenomenon in terms of people's sensitivity to the relationships among premise items. We show that a Bayesian model of category‐based induction taking premise sampling assumptions and category similarity into account complements such theories and yields two important predictions: First, that sensitivity to premise relationships can be violated by inducing a weak sampling assumption; and second, that premise monotonicity should be restored as a result. We test these predictions with an experiment that manipulates people's assumptions in this regard, showing that people draw qualitatively different conclusions in each case.