Concept

Deductive reasoning

Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning. Psychology is interested in deductive reasoning as a psychological process, i.e. how people actually draw inferences. Logic, on the other hand, focuses on the deductive relation of logical consequence between the premises and the conclusion or how people should draw inferences. There are different ways of conceptualizing this relation. According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, on the other hand, holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference. A rule of inference is a schema of drawing a conclusion from a set of premises based only on their logical form. There are various rules of inference, like the modus ponens and the modus tollens. Invalid deductive arguments, which do not follow a rule of inference, are called formal fallacies. Rules of inference are definitory rules and contrast to strategic rules, which specify what inferences one needs to draw in order to arrive at an intended conclusion.

Official source

https://en.wikipedia.org/wiki/Deductive_reasoning

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (32)

MATH-207(d): Analysis IV

The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems. ...

MATH-700: Reasoning in artificial intelligence

Large language models have raised the potential of artificial intelligence in various applications, including science and mathematics, but their reasoning capabilities remain under investigations. This class focuses on defining, measuring and improving the ...

CS-461: Foundation models and generative AI

This course covers the principles, architectures, and applications of foundation models and generative AI, including generative methods, tokenization, multi-modal learning, adaptation, prompting, and their use in reasoning, decision-making, and scientific ...

Related lectures (32)

Quantum Machine Learning: Theory and Applications

Explores quantum machine learning, representations of molecules, kernel regression, and the interplay between physics and machine learning.

Exam instructions: clear reasoning and units

Covers exam instructions emphasizing clear reasoning and units in answers, with a focus on thermodynamics.

Educational Sequencing: Granularization and Scenario Design

Explores different types of educational sequencing and scenario design.

Related publications (32)

AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking

Emmanuel Abbé

Recent studies have shown that large language models (LLMs), especially smaller ones, often lack robustness in grade school math (GSM) reasoning. In particular, they tend to experience performance drops when faced with distribution shifts, such as changes to numerical or nominal variables, or insertions of distracting clauses. A possible strategy to address this involves generating synthetic data to further "instantiate" reasoning problems on potential variations. In this work, we instead focus on the strat

2026

Understanding Implicit Schemas of Reasoning

Artificial intelligence (AI) systems, especially those powered by large language models (LLMs), are currently experiencing prosperity and rapid development. However, LLMs still show reliability deficiencies of understanding and applying knowledge in various domains or contexts. This indicates room for improvement in LLMs' capabilities of reasoning, which typically requires implicit thinking and integration of world knowledge to infer dynamic output actions or results, rather than direct recourse to memorize

EPFL2026

Tracking the Limits of Knowledge Propagation: How LLMs Fail at Multi-Step Reasoning with Conflicting Knowledge

A common solution for mitigating outdated or incorrect information in Large Language Models (LLMs) is to provide updated facts in-context or through knowledge editing. However, these methods introduce knowledge conflicts when the knowledge update fails to overwrite the model’s parametric knowledge, which propagate to faulty reasoning. Current benchmarks for this problem, however, largely focus only on single knowledge updates and fact recall without evaluating how these updates affect downstream reasoning.

Association for Computational Linguistics (ACL)2026

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Official source

https://en.wikipedia.org/wiki/Deductive_reasoning

About this result

Related courses (32)

MATH-207(d): Analysis IV

The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems. ...

MATH-700: Reasoning in artificial intelligence

CS-461: Foundation models and generative AI

Related lectures (32)

Quantum Machine Learning: Theory and Applications

Explores quantum machine learning, representations of molecules, kernel regression, and the interplay between physics and machine learning.

Exam instructions: clear reasoning and units

Covers exam instructions emphasizing clear reasoning and units in answers, with a focus on thermodynamics.

Educational Sequencing: Granularization and Scenario Design

Explores different types of educational sequencing and scenario design.

Related publications (32)

AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking

Emmanuel Abbé

2026

Understanding Implicit Schemas of Reasoning

EPFL2026

Tracking the Limits of Knowledge Propagation: How LLMs Fail at Multi-Step Reasoning with Conflicting Knowledge

Association for Computational Linguistics (ACL)2026

Related people (32)

Zsuzsanna Viktoria Szemeredi

Teaching & PhD Courses Critical thinking I HUM-425 This course will develop logical reasoning and argumentation skills to enable you to influence decision making. You will achieve this by learning how to represent and communicate your reasoning as arguments, and by continuously practicing logical reasoning and problem solving in teams. Critical thinking II HUM-484 Critical Thinking II (HUM 484) builds on concepts acquired in Critical Thinking I (HUM 425). Please read HUM

Andrea Cavallaro

Expertise I focus on machine learning for audio-visual sensing to enable systems to serve agreed purposes and improve their abilities through interactions with the environment, with other systems and with people. The goal of my research is to create the next-generation machine perception models for the effective use of sensory data, and the safe operation of autonomous systems that gain information about their environment and make decisions in partnership with humans or independently. These models are trans

Robert West

Robert West is a tenure-track assistant professor of computer science at EPFL, where he heads the Data Science Lab. In his research, he develops and applies techniques in machine learning, computational social science, natural language processing, social network analysis, and data mining. Bob also collaborates closely with the Wikimedia Foundation, in his role as a Wikimedia Research Fellow. Bob’s work has won several awards, including best/outstanding paper awards at ICWSM’21, ICWSM’19, and WWW’13, a best-paper runner-up award at WWW’16, a Google Faculty Research Award, a Facebook Research Award, a Hewlett-Packard Graduate Fellowship, and a Facebook Graduate Fellowship. He is actively involved in the research community, e.g., as an Associate Editor of ICWSM and EPJ Data Science and as a co-founder of the Wiki Workshop (held at WWW and ICWSM) and the Applied Machine Learning Days. Bob received his PhD in Computer Science from Stanford University, his MSc from McGill University, Canada, and his undergraduate degree from Technische Universität München, Germany.[Last updated: 25 Aug 2021]

Francesco Stellacci

Francesco Stellacci graduated in Materials Engineering at the Politecnico di Milano in 1998 with a thesis on photochromic polymers with Prof. Giuseppe Zerbi and Mariacarla Gallazzi. In 1999 he moved to the Chemistry Department of the University of Arizona for as a post-doc in the group of Joe Perry in close collaboration with the group of Seth Marder. In 2002 he moved to the Department of Materials Science and Engineering at the Massachusetts Institute of Technology as an assistant professor. He was then promoted to associate without (2006) and with tenure (2009). In 2010 he moved to the Institute of Materials at EPFL as a full Professor. He holds the Alcan EP Chair. Francesco was one of the recipients of the Technology Review TR35 "35 Innovator under 35" award in 2005, and the Popular Science Magazine "Brilliant 10" award in 2007. He has been a Packard Fellow starting 2005.

Antoine Bosselut

Antoine Bosselut is an assistant professor at EPFL. He leads the EPFL NLP group, which conducts research on natural language processing (NLP) systems that can model, represent, and reason about human and world knowledge. Prior to joining EPFL, he was a postdoctoral researcher at Stanford University working in the SNAP and NLP groups and a young investigator on the Mosaic project at the Allen Institute for AI . He completed his PhD at the University of Washington.

Francesco Mondada

Dr. Mondada received his M.Sc. in micro-engineering in 1991 and his Doctoral degree in 1997 at EPFL. During his thesis he co-founded the company K-Team, being both CEO and president of the company for about 5 years. He is one of the three main developers of the Khepera robot, considered as a standard in bio-inspired robotics and used by more than 1,000 universities and research centers worldwide. Fully back in research in 2000 and after a short period at CALTECH, he participated to the SWARM-BOTS project as the main developer of the s-bot robot platform, which was ranked on position 39 in the list of The 50 Best Robots Ever (fiction or real) by the Wired Journal in 2006. The SWARM-BOTS project was selected as FET-IST success story by the EU commission. He is author of more than 100 papers in the field of bio-inspired robotics and system level robot design. He is co-editor of several international conference proceedings. In November 2005 he received the EPFL Latsis University prize for his contributions to bio-inspired robotics. In 2011 he received the "Crédit Suisse Award for Best Teaching" from EPFL and in 2012 the "polysphère" award from the students as best teacher in the school of engineering. His interests include the development of innovative mechatronic solutions for mobile and modular robots, the creation of know-how for future embedded applications, and making robot platforms more accessible for education, research, and industrial development.

Viktor Kuncak

Viktor Kunčak joined EPFL in 2007, after receiving a PhD degree from MIT. Since then has been leading the Laboratory for Automated Reasoning and Analysis and supervised at least 12 completed PhD theses. His works on languages, algorithms and systems for verification and automated reasoning. He served as an initiator and one of the coordinators of a European network (COST action) in the area of automated reasoning, verification, and synthesis. In 2012 he received a 5-year single-investigator European Research Council (ERC) grant of 1.5M EUR. His invited talks include those at Lambda Days, Scala Days, NFM, LOPSTR, SYNT, ICALP, CSL, RV, VMCAI, and SMT. A paper on test generation he co-authored received an ACM SIGSOFT distinguished paper award at ICSE. A PLDI paper he co-authored was published in the Communications of the ACM as a Research Highlight article. His Google Scholar profile reports an over-approximate H-index of 38. He was an associate editor of ACM Transactions on Programming Languages and Systems (TOPLAS) and served as a co-chair of conferences on Computer-Aided Verification (CAV), Formal Methods in Computer Aided Design (FMCAD), Workshop on Synthesis (SYNT), and Verification, Model Checking, and Abstract Interpretation (VMCAI). At EPFL he teaches courses on functional and parallel programming, compilers, and verification. He has co-taught the MOOC "Parallel Programming" that was visited by over 100'000 learners and completed by thousands of students from all over the world.

Giovanni De Micheli

Expertise Design technologies for integrated systems on silicon, such as synthesis, hw/sw codesign and low-power design, as well as systems on heterogeneous platforms including electrical and biological components. Scientific Director of EcoCloud Center at EPFL Directing activities towards creating sustainable computation including AI.Designing energy-savvy data centers and edge devices. More information Please read http://si2.epfl.ch/~demichel/ Giovanni De Micheli is a research scientist in electronics and

Related units (6)

Laboratory for Automated Reasoning and Analysis

Related concepts (29)

Generalization

A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation.

Modus tollens

In propositional logic, modus tollens (ˈmoʊdəs_ˈtɒlɛnz) (MT), also known as modus tollendo tollens (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. Modus tollens takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.

Logic

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language.

Related exercises (2)

Bouncing balls

Two balls of mass m₁ and m₂ are dropped with no initial speed, one above the other, from height h. We assume that the balls stay in contact throughout their drop until they bounce on the floor. The situation can be descriped as an elastice collision between ball m₁ and the floor, immediately followed by a collision between the two balls. The balls’ radii is negligible when compared to h. There is no air friction. Answer the following questions in two cases: 1) the collision between the two balls is elastic

Car suspension problem

A car’s suspension is comfortable when it has a vertical oscillation period that our bodies are used to: the oscillation period of walking, Tu2004=u20040.8u2005s.

Find the spring constant k of the suspension in a car of mass $M = 1540\,{\rm kg}$ .
The car lowers when we place a trunk of mass $m = 70\,{\rm kg}$ in it. Find its vertical displacement.

To make the car more comfortable, we add a shock absorber/dampener that creates a friction force F⃗u2004=u2004u2005−u2005bv⃗_(z), where v⃗_(z)