Introduction to Logic-Based AI The Second Edition, Launched August 28 2025!! Instructor: Selmer Bringsjord
Table of Contents
Course Encapsulation
This course is an introduction to logic-based artificial intelligence (AI). We learn techniques for designing and engineering AIs with human-level (or higher) cognitive intelligence, enabled by automated reasoning as the basis for: planning, learning, decision-making, communicating, creativity, and perceiving. A special emphasis is placed upon giving AIs intellectual powers that are beyond the reach of large language models (LLMs) like GPT-4 and other so-called “foundation models,” which, based as they are on statistical/numerical machine learning (e.g. deep learning, which is driven by data stripped of logical meaning and structure), are congenitally (and dangerously) prone to poor performance in applications that require high precision and accuracy, and/or require formally verified correct behavior. We thus direct our attention to solving the very problem currently occupying the first-rate minds of many at companies in the AI sector of the economy, e.g. Google. Thus those who succeed in this course will be in position to offer such companies skills that are increasingly sought, but are in very short supply. We explore how to remedy the deficiencies of LLMs with AI based on computational logics, from the propositional calculus, through fragments of first-order logic crucial for the World Wide Web’s productive operation, on up to logics needed to model and simulate very high levels of human and machine intelligence. Our programming paradigm is logic programming, introduced and taught from scratch, starting slowly from so-called “Horn Logic.”
Four key aspects of the course are that:
- a crucial source of learning in this course will be the cinematic arts, primarily belletristic sci-fi films about AI/AIs;
- much of the teaching in this course will revolve around playing and analyzing fun games of logic and logical reasoning;
- coverage of AI-relevant quantum computing, analyzed by way of formal logic; and
- coverage as well of not only “straight” AI, but also so-called artificial general intelligence (AGI).
Prerequisites: Standard high-school math progression with Algebra 2 (or equivalent) through some calculus; some prior study of formal logic and proofs; and some prior programming (in at least one or more procedural or functional languages; no prior experience with logic programming necessary). No particular courses must’ve been taken in order to qualify.
Visitors: The course will occasionally be simulcast in such a way that some special visitors will be allowed to attend by Zoom (up to a size cutoff). This contingent will be determined by the policy of first come, first served, implemented when the Zoom links are published later, on an expanded version of the present page.
Questions? Email SB at
Selmer.Bringsjord@gmail.com
Syllabus
Version 0907251400NY of the syllabus for the inaugural version of
Fall 2025 ILBAI is available here.
Class-Day Content
- August 28 2025: Preliminary Orientation (S Bringsjord)
- September 4 2025 Course Mechanics/Logistics Re-Review; Blade Runner vs CAPTCHA, the Turing Test, & Worldcoin (S Bringsjord)
After revisiting the slide deck from last time, the syllabus briefly re-projected and presented, and discussed, in detail. Assignment #1 — to watch BR — leads here to an open, free-wheeling discussion of the movie, and, minimally, three topics (authenticaion of humans in today’s fintech world, CAPTCHA, the Turing Test; machine conscioiusness; and the limits of machine intelligence)
- September 8 2025: What is Logic-Based AI?; Whirlwind History of Logic-Based AI — With Skepticism About The Singularity Derived Therefrom (S Bringsjord)
After a look at some AI in The News, and some discussion of Blade Runner (and a watching of the Tears-in-the-Rain scene), we review and affirm the basic, abstract perception2computation2action loop that is the essence of the life of an intelligent agent, and point out that in the logic-based case this computation consists in reasoning over content in logics. We then take a time-traveling tour of computational formal logic and AI, from Euclid, three centuries BC, to Aristotle and his logics (the first logics created by humankind) to — possibly? — The Singularity in our future. Along the way we note that Leibniz, peerless polymath and autodidact, is the inventor of modern formal logic, and that at AI’s DARPA-sponsored dawn in 1956, the automated reasoner LogicTheorist stole the show. The presentation ends with Bringsjordian skepticism about The Singularity in light of (Turing-level) machine impotence in the face of the Entscheidungsproblem.
- September 11 2025: The Failure of Deep Learning; GPT-4o Bites the Dust (S Bringsjord)
We challenge GPT-4o (as well as the recent LRM GPT-5) with some problems that are cakewalks for logic-based AI systems, and observe well its abject failure. The problems used serve to provide the start of a gentle introduction to the logic known as the propositional calculus, or just \(\mathscr{L}_{pc}\) — and we also take a look ahead to the problem of layered quantification for (artificial) neural network-based AI, which 45 years ago was laid down as the chief challenge to succh AI by the logicians. This challenge remains completely unmet today. We note, quickly, that the AIs in HyperSlate®, known as oracles, have no trouble at all with the problems that cripple GPT- 4o — including Moriarty’s fiendish red-or-blue-wire? bomb challenge.
- A video showing the use of the PC provability oracle in HyperSlate® solving the “NYS 3” logic problem is available here.
- September 18 2025 Moriarity Bomb Challenge #2; Final-Project Landscape (S Bringsjord)
We consider a second, harder bomb challenge from the nefarious Prof. Moriarity, one involving now three wires, not just two. We also go over the final-project options, in connection with relevant supporting technology to accomplish them. Unfortunately, screen
- September 22 2025: PPC = ZOL via Return Creating Zoombinis (S Bringsjord)
Selmer creates three Zoombinis in Logical Journey of the Zoombinis; each of the three has four attribute types, corresponding to choices the human player makes regarding how to “bring to life” new Zoombinis. Then, he shows formal inferences in HyperSlate® that are distinctive of the Pure Predicate Calculus = Zero-Order Logic. A hotlink to the HyperSlate® workspace in play is provided in the slide deck.
- September 25 2025:
- Artificial General Intelligence, & The Landscape That Includes It (James Oswald)
- Natural-Deduction ProofStrategies in HyperSlate (James Oswald)
Lecturer and AGI expert James Oswald explains whayt AGI, Artificial General Intelligence, is, what the dominant theories thereof today are, and what sort of futures are predicted by AGI theoreticians. In addition, he then proceeds to present strategies for building proofs, using plenty of screenshots from use of the system to detail the anatomy of these strategies.
- September 29 2025: Human Disemployment & The MiniMaxularity (S & A Bringsjord)
Bringsjords here discuss the MiniMaxularity (not to be confused with the Singularity!), the fast-approaching point in time when the embryonic competence of AIs of today at the “laboratory level” mature, and hence do many human jobs to the point where they match (and in some cases exceed, even greatyly) human performance in these jobs.
- October 2 2025: First-Order Logic = FOL, Part 1; and the First (Logic) Programmer (S Bringsjord)
Here begins coverage of FOL = \(\mathscr{L}_1\). We start by taking note of the vast intellectual canyon separating nonhuman animals and humans, created in significant part by their inability to reason with quantifiers, versus our ability to do so. We then explore the fragment of FOL invented by Aristotle over two millennia ago, which allows only a single quantifier into each proposition (e.g. “All foobers are sneepers,” which has when logicized a single universal quantifier (
forallin our s-expressions) and no others). Aristotle wrote logic programs that had only two lines, specifically two such propositions; and in addition he allowed a query against these programs in the form of a third proposition, the question being whether or not the third follows deductively from the two-line program. Next and finally, we explore, using the logic-based AI in HyperSlate® (specifically oracles operating at the level of FOL) the fascinating items on the Deductive Flexibility Test from the Reasoning Research Group at Polands’s Adam Mickiewicz University. - October 6 2024: First-Order Logic = FOL, Part 2 (S Bringsjord)
After our traditional look at some ILBAI-relevant news in the popular media, we move to Part 2 of FOL = \(\mathscr{L}_1\), in hands-on, dynamic fashion in HyperSlate®. We further explore, using the logic-based AI in HyperSlate® (specifically oracles operating at the level of FOL) the fascinating Deductive Flexibility Test from the Reasoning Research Group at Polands’s Adam Mickiewicz University. Coverage of the inference schema
universal introis provided in the slide deck; full coverage is in our e-textbook. - October 9 2025: First-Order Logic = FOL, Part 3 (S Bringsjord)
After our traditional look at some ILBAI-relevant news in the popular media, specifically the prediction that 64% of human jobs will be taken over by AIs (asserted by Vinod Khosla), and after taking a look at how the latest member of the GPT-/k/ series does on self-referential sentences, we move to Part 3 of FOL = \(\mathscr{L}_1\), once again in hands-on, dynamic fashion in HyperSlate®. We further explore, using the logic-based AI in HyperSlate® (specifically oracles operating at the level of FOL) the fascinating Flexibility Test from the Reasoning Research Group at Polands’s Adam Mickiewicz University. This time, students must first logicize a DFT item from scratch, before tackling with help from the AI oracle in HyperSlate®. Finally, the Colonel-West-Criminal? probelm from AIMA 4E Chap 9 is presented, and issued to students. Coverage of the inference schema
existential elimis provided in the slide deck; full coverage is in our e-textbook. - October 13 2025: No Class: Columbus Day/Indigenous People’s Day
- October 16 2025 The DFT+; On to Intensional Logics; Real Learning
The full title of this class is, and yes, it’s admittedly quite a mouthful: “FOL Problems on HG®; ‘Aristotle’ Problems & DFT+ From You in Logicist AI Work; Intensional Logic & ‘The TOS’ Changeling’; Real Learning Glimpse & Paper.” We first
- Take a look at some FOL problems in HG®.
- Explain the Selmer-invented DFT+.
We then pass to a general introduction, using the robot Blinky and a shell game, along with the False Belief Test (FBT) at level 5 and beyond, to the crucial difference between extensional logics versus intensional logics. The logics \(\mathscr{L}_{pc}\), \(\mathscr{L}_0\), \(\mathscr{L}_1\), \(\mathscr{L}_2\), \(\mathscr{L}_3\) are all extensional. Now we move to the intensional category, which includes modal logics. The quantified modal logic \(\mathcal{DCEC} is mentioned\).
- October 20 2025 Live Work/Proof Discovery on DFT/DFT+ Problems Using Paper & Pen/Pencil, and HyperSlate® (Selmer Bringsjord)
- October 23 2025 Live Work/Proof Discovery on HyperGrader® Problems in HyperSlate® (James Oswald)
Dr-to-be James Oswald provides hands-on, live coverage & help etc for the current live HGproblems, in order to gry to bring those in attendance closer to tropies. To help with modal-logic problems (doable in the workspaces devoted to them in HS), James makes this of this slide deck. A Personalized “positronic-brain” problem is scheduled to be released into all accounts before class, so a final part of the meeting is devoted to advice & discussion of these problems, for hotshots.
- October 27 2025 Live Work/Proof Discovery on HyperGrader® Problems in HyperSlate® (James Oswald & Selmer Bringsjord)
This is a four-part class, predominantly taught by James Oswald; it unfolds as follows.
- 5 minutes to announce the plan & say a few words about our Overleaf-based tracking of final projects, the for-LLMizing English-izing of positronic-brain problems, and the ShadowProver & Spectra release to all registrants.
- 15 minutes for Selmer to give a lightning version of his (with Naveen Sundar G, Brian McDermott, & A Bringsjord) “Ethically Permissible Pursuit of Quantum Consciousness.”
- 80 minutes for James Oswald to present on automated planning in AI, using the slide deck here. Students learn how to formalize state and actions via a Blocksworld and are introduced to some of the math behind planning in the STRIPS formalism. Students also learn how to write simple PDDL.
- 10 minutes for discussion between James & Selmer & class re. automated “cognitive” planning.
Cinematic Assignments
- For discussion in class on Thu Sep 4 2025, watch original Blade Runner (Director’s Cut if at all possible) film. Read one or two serious articles in the media (e.g. this from WSJ; there are numerous such, outside of any paywalls) about about Altman’s Worldcoin initiative. We shall discuss in class on Thu Sep 3.
- For discussion in class on Thu Oct 16, watch The Thinking Game. This is a documentary.