From Abstract to Accessible: Rethinking Logic Education with Visual and Interactive Tools

Ensuring equitable access to education requires innovative methodologies and pedagogical tools that accommodate diverse learning needs. In Logic education, traditional approaches often rely on abstract and text-heavy content, which can present significant challenges for deaf students. Recognizing this gap, the LogLibras project focuses on developing visual and interactive didactic materials, designed to support the specific educational and communicative needs of deaf learners.

This article presents the progress made in creating inclusive educational resources for teaching Logic, with a strong emphasis on visual accessibility and drawing inspiration from the principles of universal design for learning, while acknowledging the specific needs of different student groups (LogLibras Project). The materials developed are structured with highly visual content, which will be integrated into video lessons recorded in Brazilian Sign Language (Libras), ensuring a more effective learning experience for deaf students. Additionally, to maximize the impact of these resources, step-by-step instructional guides will be provided to educators, facilitating the easy replication of these materials in classroom settings.

By fostering the adoption of these inclusive strategies, LogLibras enhances the accessibility of Logic education while promoting collaborative learning among all students. The project aims to create an educational environment where diverse learners can interact and construct knowledge together. This article explores the methodologies employed, the pedagogical foundations behind these materials, and the future directions of the LogLibras initiative.

LogLibras: A Visual and Interactive Approach to Inclusive Logic Education

Developed with funding from CNPq (Process 420284/2022-2), the LogLibras project aims to make Logic education more accessible through visually structured and interactive materials designed for deaf students. Traditional approaches often rely on text-heavy content, which can be challenging for learners who process information primarily through visual means. LogLibras addresses this gap by prioritizing gesture-visual didactic resources that maintain conceptual rigor while enhancing accessibility and engagement.

To further expand its impact, the project incorporates educational technologies, combining illustrated concept maps, structured diagrams, and interactive media to make abstract logical concepts more tangible. These resources are not only used in video lessons in Libras, but are also designed for easy replication in classroom activities, supported by step-by-step instructional guides for educators.

By emphasizing visual learning, interaction, and structured accessibility, LogLibras redefines how Logic can be taught in an inclusive educational setting. The methodology fosters collaboration among all students—both deaf and hearing—encouraging an environment where diverse learners can engage meaningfully with logical reasoning and critical thinking.

The Collaborative Network Behind LogLibras: From Biology to Philosophy

In 2019, the enrollment of a deaf student in a high school program at the Federal Institute of São Paulo, campus Votuporanga (IFSP-Votuporanga) highlighted the need for curriculum adaptations to ensure full participation in classroom activities. Brazilian legislation, notably the Brazilian Inclusion Law (Law No. 13,146/2015), among other legal frameworks, guarantees the inclusion of deaf students in regular education settings. However, it does not necessarily provide structured resources or adequate support for educators, often leaving them responsible for developing their own materials, a task that can be challenging without institutional backing.

Faced with this reality, Biology teacher Anna Isabel Nassar Bautista initiated the LIBIO project, aiming to make Biology content more accessible through video lessons in Brazilian Sign Language (Libras). However, the project quickly encountered two significant challenges: the lack of a comprehensive technical sign dictionary for Biology and the need to create new signs for specialized terms. To address these issues, the team collaborated with the Accessibility Support Center (NAPNE) at IFSP-Votuporanga, led by Lucimar Bizio, working alongside the deaf community to develop a systematic glossary of technical terms. This effort significantly improved the accessibility of the materials, benefiting students, interpreters, and future educators.

One of LIBIO’s key strategies was to incorporate visual diagrams and illustrations to represent biological concepts, such as photosynthesis or cellular organelles (Fig. 1), making the content more comprehensible for deaf students. The use of visual aids proved highly effective, reinforcing the role of gesture-visual learning in the adaptation of scientific subjects for Libras.

Inspired by LIBIO’s success, Philosophy teacher João Antonio de Moraes launched the FiloLibras project, adapting philosophical content to Libras. However, unlike Biology, which could rely on visual representations of natural processes, Philosophy presented a different challenge: how to effectively convey abstract concepts such as Truth and Validity in a primarily visual format.

To tackle this issue, FiloLibras expanded into an interdisciplinary initiative, bringing together specialists from different branches of Philosophy to explore how traditional teaching tools from their respective fields could be adapted to a gesture-visual methodology. Within this collaboration, Logic specialist Rafael R. Testa developed a Libras-based lesson on Logic, using visual tools to translate logical structures into an accessible format. This experience demonstrated the potential for expanding the approach to a more structured initiative focused entirely on Logic education, inspiring the development of what would later become LogLibras.

Now headquartered at the Centre for Logic, Epistemology, and the History of Science of University of Campinas (CLE-Unicamp) and co-managed by IFSP-Votuporanga, LogLibras builds on this interdisciplinary foundation. By integrating visual learning methodologies, interactive tools, and structured pedagogical frameworks, the project redefines how Logic can be taught in inclusive classrooms, fostering collaboration between deaf and hearing students and making abstract reasoning more accessible through innovative educational strategies.

Visual Pedagogy: The Foundation of LogLibras Technologies

The visual pedagogy that underpins LogLibras’ technological developments is deeply rooted in Deaf culture, incorporating visual storytelling, educational games, metaphors, and concept maps to align with the natural cognitive and communicative processes of deaf students. Rather than merely transposing information from spoken language into sign language, LogLibras maps logical structures onto visual frameworks, ensuring that complex concepts are conveyed in a way that is both intuitive and accessible.

Drawing on Vygotsky’s sociocultural theory of learning, LogLibras acknowledges that knowledge is not acquired in isolation, but constructed through social and linguistic interactions. While Vygotsky originally emphasized the role of spoken language in cognitive development, his ideas have been reinterpreted in the field of Deaf Studies, where sign languages serve as the primary medium for knowledge construction. In this view, visual learning is not merely an adaptation for deaf students—it is an equally robust and valid cognitive pathway for abstract reasoning and conceptual understanding.

Beyond its impact on deaf education, LogLibras also embraces multimodal learning, which integrates visual, spatial, textual, and interactive elements to enhance engagement for all students. By offering multiple modes of representation, LogLibras fosters a dynamic, inclusive, and engaging learning environment, bridging gaps between deaf and hearing students while promoting a richer educational experience for everyone.

Simple Visual Teaching Technologies

Illustrations and Visual Metaphors

One of LogLibras’ core strategies is the use of visual metaphors to simplify abstract concepts in Logic, making them more intuitive for deaf students and visual learners. By leveraging recognizable images and structured analogies, these metaphors help bridge the gap between formal logical structures and real-world reasoning.

A striking example is the use of M.C. Escher’s artwork Waterfall to illustrate logical inconsistencies. At first glance, the image appears to depict a coherent and continuous water flow. However, upon closer inspection, one realizes that the structure is impossible—the water seemingly defies gravity in a paradoxical loop. This illusion serves as an engaging introduction to logical fallacies and errors in reasoning, demonstrating how something may appear valid at first but collapse under closer scrutiny.

This analogy is inspired by the one employed by Irving Copi in Introduction to Logic, where visual representations are effectively used to reinforce abstract logical concepts. While Copi does not explicitly discuss the use of metaphors in his illustrations, their pedagogical function as conceptual aids is evident.

Another powerful visual metaphor represents logical premises as pillars supporting a conclusion. If the reasoning is valid, the structure remains stable and intact. However, if one of the premises is weak or flawed, the structure collapses—visually emphasizing the importance of sound logical argumentation. This method provides students with an intuitive grasp of inference structures, reinforcing their ability to evaluate argument validity effectively.

Incorporating visually structured representations, such as diagrams, into logic education not only enhances abstract reasoning skills but also serves as a direct and effective means of representing logical concepts. This perspective is strongly supported by Jon Barwise and John Etchemendy in their work on Hyperproof—a precursor to their later project Tarski’s World, which will be discussed below. In Hyperproof, they demonstrate that diagrams can function as integral components of formal proofs, complementing traditional symbolic representations rather than merely serving as heuristic aids. By leveraging these visual tools, learners can engage with logical inference in a manner that is both intuitive and formally rigorous, thereby expanding the landscape of logical reasoning beyond the confines of purely symbolic methods.

Diagrams as Tools for Logical Reasoning

Diagrams are fundamental tools in logic education, not only aiding comprehension but also serving as rigorous representations of logical structures. Rather than being mere heuristic devices, they provide precise and formal means of reasoning, allowing learners to visualize and manipulate logical relationships intuitively. Two widely used types, Euler diagrams and Venn diagrams, offer distinct yet complementary approaches to expressing categorical statements and evaluating logical arguments.

Euler Diagrams: Illustrating Specific Logical Relationships

Euler diagrams are particularly useful for visualizing categorical statements that involve logical quantifiers such as “All”, “None”, “Some”, and “Some … not”. Unlike Venn diagrams, which represent all possible intersections, Euler diagrams depict only the actual relationships between sets, making them an intuitive tool for understanding logical structures.

Visualizing Logical Statements Through Euler Diagrams

The following four fundamental logical statements can be effectively illustrated using Euler diagrams:

1. “All A are B” (Universal Affirmative, A-form):
   • The set A is fully contained within set B, indicating that every element of A belongs to B.
   • Example: “All mammals are animals.” The circle representing Mammals is entirely inside the circle for Animals.
2. “No A are B” (Universal Negative, E-form):
   • The sets A and B are drawn as completely separate circles, illustrating that no elements of A are found in B.
   • Example: “No reptiles are mammals.” The Reptiles and Mammals circles do not overlap.
3. “Some A are B” (Particular Affirmative, I-form):
   • The sets A and B partially overlap, indicating that at least one element of A also belongs to B.
   • Example: “Some birds are flightless.” The Birds and Flightless Animals circles share an overlapping region.
4. “Some A are not B” (Particular Negative, O-form):
   • The set A is partially inside B, but with a distinct portion outside B, showing that some elements of A do not belong to B.
   • Example: “Some pets are not dogs.” The Pets circle partially overlaps with Dogs, but also extends beyond it, indicating pets that belong to other species.

Having established how Euler diagrams represent logical quantifiers, we now illustrate their application in a simple categorical syllogism. By visually mapping the relationships between sets, these diagrams help clarify how premises lead to a valid conclusion.

Example:

1. Premise 1: All men are mortal
2. Premise 2: Socrates is a man.
3. Conclusion: Therefore, Socrates is mortal.

In this case, the set of ‘Men’ is completely contained within the set of ‘Mortals’, representing the universal statement that all men are mortal. The individual ‘Socrates’ is placed within the ‘Men’ set, visually confirming that he must also belong to the ‘Mortals’ set. This structured representation allows students to intuitively grasp how categorical statements and logical deductions function, reinforcing their understanding of valid inference patterns through a clear, visual framework.

In the next section, we introduce a general method for evaluating syllogisms using Venn diagrams, which provides a systematic approach to verifying logical validity across a broader range of arguments.

Venn Diagrams: A Systematic Method for Evaluating Syllogisms

Venn diagrams and Euler diagrams are both valuable tools for representing logical relationships, but they differ in scope and application. Euler diagrams depict only the relationships that actually exist between sets, omitting non-existent intersections, making them well-suited for intuitive representations. Venn diagrams, on the other hand, illustrate all possible logical relations between sets, even if some intersections are empty. This makes them particularly useful for evaluating categorical syllogisms, as they provide a complete framework for testing logical validity.

Representing Categorical Propositions with Venn Diagrams

Two-circle Venn diagrams are commonly used to represent categorical statements, illustrating the relationships between two sets:

1. Universal Affirmative (“All S are P”)
   • The non-overlapping part of S is shaded, indicating that there are no elements in S that are not in P.
   • Example: “All dogs are mammals.” The Dogs circle is entirely within the Mammals circle.
2. Universal Negative (“No S are P”)
   • The intersection between S and P is shaded, indicating that they share no members.
   • Example: “No reptiles are mammals.” The Reptiles and Mammals circles do not overlap.
3. Particular Affirmative (“Some S are P”)
   • An x is placed in the overlapping region of S and P, showing that at least one element is in both sets.
   • Example: “Some birds are flightless.” An x appears in the overlap of Birds and Flightless Animals.
4. Particular Negative (“Some S are not P”)
   • An x is placed in the non-overlapping part of S, indicating that some elements in S are not in P.
   • Example: “Some pets are not dogs.” An x appears in the Pets region that does not intersect with Dogs.

Applying Venn Diagrams to Categorical Syllogisms

To evaluate categorical syllogisms, which involve three sets, three-circle Venn diagrams are used. Each circle represents one of the three terms in the syllogism:

• The minor term (S) – the subject of the conclusion
• The major term (P) – the predicate of the conclusion
• The middle term (M) – the term that appears in both premises

Steps to Test a Syllogism Using Venn Diagrams

1. Diagram the premises, following these rules:
   • Use shading to represent universal statements (All A are B and No A are B).
   • Use x-marks for particular statements (Some A are B and Some A are not B).
2. Check if the conclusion is already represented in the diagram:
   • If the conclusion appears, the syllogism is valid.
   • If the conclusion is not visually confirmed, the syllogism is invalid.

Example 1: A Valid Syllogism

• Premise 1: All Greeks are human.
• Premise 2: No humans are immortal.
• Conclusion: Therefore, no Greeks are immortal.
• The “Greeks” circle is entirely inside the “Humans” circle, since all Greeks are human.
• The “Humans” and “Immortals” circles do not overlap, showing that no humans are immortal.
• Since the intersection between “Greeks” and “Immortals” is shaded, the conclusion is confirmed, making the syllogism valid.

Example 2: Another Valid Syllogism

• Premise 1: Some mammals are carnivores.
• Premise 2: All mammals are animals.
• Conclusion: Therefore, some animals are carnivores.
• The “Mammals” circle is entirely inside “Animals”.
• An x is placed in the overlap of Mammals and Carnivores.
• Since that x is also inside “Animals”, the conclusion is visually represented, confirming validity.

Example 3: An Invalid Syllogism

However, there is no direct connection between sages and soothsayers, meaning that the conclusion is not visually confirmed. The syllogism is invalid.

Premise 1: Some sages are not seers.

Premise 2: No seers are soothsayers.

Conclusion: Therefore, some sages are not soothsayers.

The “Seers” and “Soothsayers” circles do not overlap.

An x is placed in the “Sages” circle, outside of “Seers,” indicating that some sages are not seers.

Gamification in Logic Education

Gamification -the incorporation of game mechanics such as interactive challenges, structured puzzles, and competitive problem-solving – has emerged as an effective pedagogical tool for enhancing engagement and facilitating abstract reasoning. In Logic education, where students often struggle with symbolic representations and formal derivations, gamified approaches provide an intuitive and exploratory entry point to logical thinking.

By integrating interactive methodologies, LogLibras employs game-based strategies that bridge formal logic with tangible, visually structured experiences, making the learning process more accessible, dynamic, and engaging. Below, we examine three key gamification strategies utilized in the project.

Lewis Carroll’s Game of Logic: A Structured Approach to Categorical Reasoning

One of the earliest educational tools designed to introduce students to logical reasoning through gameplay was Lewis Carroll’s Game of Logic. Published in 1886, this game was developed to illustrate the mechanics of categorical syllogisms through a structured visual method rather than through purely symbolic manipulation.

Structure and Gameplay:

• The game consists of a diagrammatic representation divided into regions corresponding to categorical classes (e.g., mammals, carnivores, lions).
• Colored tokens are placed in specific areas of the diagram to indicate the presence or absence of elements within these logical categories.
• By manipulating the placement of tokens, players analyze premises and test the validity of syllogistic conclusions in a step-by-step manner.

The Game of Logic was adapted within LogLibras to facilitate categorical reasoning through a highly visual, interactive experience. By integrating this tool into classroom activities, students engage in a structured approach to logical deduction, allowing them to internalize the rules of syllogistic inference without solely relying on algebraic formalism.

Logical Puzzles: Deduction Through Narrative-Based Reasoning

Logical puzzles provide a powerful mechanism for introducing students to formal logic through structured reasoning challenges. LogLibras incorporates narrative-driven logic puzzles, particularly those inspired by Raymond Smullyan’s Knights and Knaves puzzles, which require students to deduce truth values based on self-referential statements.

Example:

A traveler encounters two individuals on an island where:

• Knights always tell the truth.
• Knaves always lie.

One of them states: “At least one of us is a Knave.” The other remains silent.

Logical Resolution:

• If the speaker were a Knight, then their statement would be true, meaning that at least one of them must be a Knave – which contradicts itself.
• Therefore, the first speaker must be a Knave, and the silent individual must be a Knight.

These types of puzzles train students in propositional logic, truth tables, and logical consistency, introducing fundamental concepts such as negation, implication, and hypothetical reasoning in an engaging and problem-solving-oriented way.

Tarski’s World: A Visual Approach to First-Order Logic

Another interactive logic tool that LogLibras incorporates is Tarski’s World, a game-based environment for exploring first-order logic through structured spatial reasoning. Originally developed by Jon Barwise and John Etchemendy, the game allows students to construct and evaluate logical statements within a formally defined world.

Game Mechanics and Learning Objectives:

• The world consists of a grid populated by geometric objects (cubes, spheres, pyramids) of varying sizes and colors.
• Students must analyze logical statements—e.g., “There exists a small cube next to a large sphere.”
• The goal is to validate or refute these statements based on the spatial relationships of the objects in the game world.

To expand accessibility, LogLibras developed a physical adaptation of Tarski’s World, replacing the digital-only environment with a tangible logic board:

• Students manipulate physical geometric objects to construct scenarios that reflect logical constraints.
• Logical statements are provided in formal notation, and students must verify their truth values based on the physical arrangement.

By transitioning from abstract symbolic logic to spatial reasoning, this adaptation reinforces the principles of first-order logic in an intuitive and exploratory manner.

Educational Robotics: Merging Technology and Logic

Educational robotics has gained increasing recognition as a pedagogical tool capable of enhancing logical reasoning through hands-on experimentation. By bridging abstract logic with tangible, interactive problem-solving, robotics provides students with immediate feedback on logical structures, reinforcing their understanding of formal reasoning, computational thinking, and algorithmic processes.

Logic Gates Educational Kit: A Hands-On Exploration of Boolean Logic

Boolean logic, the foundation of digital circuits and computational reasoning, is often introduced through truth tables and symbolic expressions. While essential, these methods can feel abstract and disconnected from practical applications. The Logic Gates Educational Kit developed in LogLibras bridges this gap, allowing students to physically construct Boolean circuits and observe logical operations in real time.

Structure and Functionality:

• The kit consists of electronic components—logic gates (AND, OR, NOT, XOR, etc.), input switches, and LED outputs.
• Students build logic circuits step by step, using wiring and connections to test different logical statements.
• The LED lights serve as truth indicators:
  • If a statement evaluates to true, the LED turns on.
  • If the statement is false, the LED remains off.

By manipulating circuits and observing immediate visual feedback, students gain an intuitive understanding of Boolean operations, reinforcing key concepts such as conjunction, disjunction, negation, and exclusive-or logic. This hands-on engagement enhances retention, making abstract logical principles more concrete and directly applicable to computational thinking.

Rubik’s Cube Solving Robot: Demonstrating Logical Deduction in Action

Algorithmic reasoning is a core component of logic, yet its applications can often seem detached from real-world problem-solving. To make structured deduction tangible and interactive, LogLibras integrates a Rubik’s Cube-solving robot built with LEGO Mindstorms, primarily based on the MindCuber project. This robotic system illustrates how complex problem-solving can be broken down into structured inference rules, reinforcing logical reasoning, algorithmic thinking, and computational problem-solving in an engaging and accessible way.

The scrambled Rubik’s Cube represents the initial premises of a logical problem, with each mixed color configuration serving as input data. The robot, equipped with color sensors, analyzes the cube’s state and feeds these conditions into a pre-programmed solving algorithm, which determines the logical sequence of moves necessary to reach the solved state. Step by step, the robot executes precise transformations, ultimately restoring the cube to its completed form—an elegant demonstration of how algorithmic thinking and deductive logic operate in practice.

A key aspect of this approach is the use of visual programming, making logical structuring accessible to students regardless of prior coding experience. The robot is programmed using EV3-G, the graphical programming language native to LEGO Mindstorms EV3, which provides an intuitive block-based interface that allows students to focus on the logical flow of instructions rather than syntax complexities. In addition to EV3-G, LogLibras incorporates Scratch and other visual programming environments, reinforcing computational thinking while broadening students’ exposure to different logical frameworks.

By engaging directly with the robot, students do more than observe abstract logical principles—they experience them. The process of breaking down complex problems into structured sequences fosters an intuitive grasp of deductive reasoning, allowing learners to see how logical inference operates dynamically. This hands-on approach not only enhances engagement and retention but also bridges the gap between formal logic and real-world applications, showing that structured reasoning underpins problem-solving across multiple domains.

Final Remarks: Expanding the Frontiers of Inclusive Logic Education

The LogLibras project represents a significant step forward in making Logic education more accessible, not only for deaf students but for diverse learners who benefit from multimodal and visual learning strategies. By integrating diagrams, gamification, robotics, and interactive methodologies, we have demonstrated that logical reasoning can be taught beyond the constraints of traditional, text-heavy approaches, fostering a more engaging and inclusive learning experience.

However, this is just the beginning. The commitment to developing innovative pedagogical tools for Logic education extends beyond the LogLibras project itself. The methodologies and resources created here lay the foundation for a broader vision: the establishment of a Logic Education Laboratory at the Center for Logic, Epistemology, and the History of Science (CLE-Unicamp). Such a laboratory would serve as a hub for research, experimentation, and dissemination of inclusive logic teaching strategies, embracing the principles of universal design to ensure that logical reasoning is accessible to all students, regardless of their linguistic or cognitive backgrounds.

By continuing to refine and expand these approaches, we aim to redefine how Logic is taught, making it not only more inclusive but also more dynamic and engaging. Logic, at its core, is about clarity, structure, and reasoning, and it is only fitting that our pedagogical approaches reflect these same ideals—adapting to the diverse ways in which human minds engage with knowledge.