Introduction to Logic-Based AI
The Inaugrual Edition, Launched September 3 2024!!
Instructor: Selmer Bringsjord

Course Encapsulation

Syllabus

Class-Day Content

• August 28 2024: Preliminary Orientation (A Bringsjord)
  

• September 3 Course Mechanics/Logistics; Blade Runner vs. Worldcoin (S Bringsjord)
  

  After revisiting the slide deck from last time, the syllabus projected and presented, and discussed, in detail. Assignment #1 discussed — and will be returned to next class (Sep 5).

• September 5 2024: 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 9 2024: The Failure of Deep Learning; GPT-4o Bites the Dust (S Bringsjord)
  

  We challenge GPT-4o 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 12 2024 The Propositional Logic via Logical Journey of the Zoombinis (S Bringsjord)
  

  We look more formally at the propositional calculus, its underlying grammar, and s-expressions that will be used in HyperSlate^®. Then we see how this calculus can be brought to life by play in Zoombinis, and use of HyperSlate^®.

• Setember 16 2024 Propositional Logic and HyperSlate (James Oswald)
  

  Lecturer James Oswald gives a tour of elementary but edifying problems in the propositional calculus for those learning logic-based AI, and uses in doing so logic-based AI itself as a key pedagogical asset: viz. the prop-calc provability oracle in HyperSlate^®.

• September 19 2024: Zeroth-Order Logic and HyperSlate (James Oswald)
  

  Lecturer James Oswald gives a tour of elementary but edifying problems in the propositional calculus for those learning logic-based AI, and uses in doing so logic-based AI itself as a key pedagogical asset: viz. the prop-calc provability oracle in HyperSlate^®.

• September 23 2024: Artificial General Intelligence (James Oswald)
  

  Lecturer and AGI expert James Oswald explains what AGI, Artificial General Intelligence, is, what the dominant theories thereof today are, and what sort of futures are predicted by AGI theoreticians.

• September 26 2024: Human Disemployment & The MiniMaxularity (A Bringsjord)
  

  Alexander Bringsjord discussed the MiniMaxularity (not to be confused with the Singularity!), the fast-approaching point in time when the embryonic competence of AIs of today to do many human jobs has developed to the point where they match (and in some cases exceed, even greatly) human performance in these jobs.

• September 30 2024: First-Order Logic = FOL, Part I; 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 (forall in 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 3 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 Flexibility Test from the Reasoning Research Group at Polands’s Adam Mickiewicz University. Coverage of the inference schema universal intro is provided in the slide deck; full coverage is in our e-textbook.

• October 7 2024: 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^®. Coverage of the inference schema existential elim is provided in the slide deck; full coverage is in our e-textbook.

• October 10 2024 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

  1. Take a look at some FOL problems in HG^®.
  2. 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 modal logics \(\mathcal{DCEC} is mentioned\).

• October 14 2024: No Class: Columbus Day/Indigenous People’s Day
  

• October 17 2024 On Connections Between the Formal Science of Cognition and Quantum Computing (QC) (Selmer Bringsjord)
  

  Using HyperSlate^® to bring things to demonstrable, computational life, S Bringsjord tackles the questions:

  • Why build and use a quantum computer?
  • Is the only viable rationale for doing so rooted in complexity theory (as Aaronson has claimed)?
  • Or does quantum computation make sense to pursue because the study of human cognition, particularly the part of it devoted to decision-making, requires quantum probability, as Busemeyer has claimed?

  Selmer provides and justifies answers to these three questions.

• October 21 2024 Live Work on DFT/DFT+ Problems Using Paper & Pencil, and HyperSlate^® (Selmer Bringsjord)
  

• October 24 2024 Robot Consciousness in the Context of the PAID Problem (Selmer Bringsjord)
  

  The field of AI has long been marginally interested in whether AIs can be conscious. But the advent of Generative AI has transformed slight interest into — at least for some — deep concern. One sign of this is the increasing frequency with which people in AI and cognate fields (e.g. computational cognitive science) these days claim that some artificial agents are conscious. But for starters, what is consciousness? We take note of the fact that there are unfortunately multiple kinds of consciousness in the relevant literature [e.g. phenomental consciousness, which centers around feelings and emotions, and is these days sometimes referred to (unknowingly) by journalists by the word ‘sentience’; versus cognitive consciousness, from S Bringsjord and NS Govindarajulu, which is accompanied by a system, \(\Lambda\), for measuring the level of c-consciousness in an agent, whether human, artificial, or alien.

• October 28 2024 The Science of Intelligence: AIXI and/versus UCI (Selmer Bringsjord on UCI; James Oswald on Legg-Hutter/AIXI)
  

  Psychologists have for a rather long time expended quite a bit of effort studying human (and, to a degree, animal) intelligence. It seems that by any metric this study has been of questionable worth; certainly it has been plagued by lack of agreement as to what intelligence is, and has often proceeded by way of leaving intelligence to be identified with a mysterious, undefined factor-analytic concept: viz. g. (Psychologists thus speak e.g. of “g-loaded” intelligence tests.) Fortunately, recently AI researchers have established a new and rigorous science of intelligence — one based in significant part on computation and formal elements of the discipline of AI. In this class, an overview of two paradigms in the science of intelligence are presented: Universal Cognitive Intelligence (UCI) from S Bringsjord et al.; and Legg-Hutter/AIXI from Hutter et al.

• October 31 2024 Automated Planning, an Overview (James Oswald)
  

  James Oswald gives an introductory overview of automated planning. 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.

• November 4 2024 As AIs Disemploy and Buy Us, They Steal Our Dignity. What’s To Be Done? (Selmer Bringsjord & Alexander Bringsjord)
  

  Kant held that human persons can never have a “market price,” because while the merely instrumental goods humans purchase and consume in the market have their prices set by the vicissitudes of supply, demand, and — in controlled economies — edict, humans themselves have a singular kind of intrinsic dignity (German Würde/). Whether or not Kant is correct, 21st-century AI appears to be turning this claim on its head; primarily, at least as we see it, by not only increasingly disemploying human workers in general, but specifically by steadily advancing toward a time when AIs, in the few cases where human labor rates are so low that AIs and robots cannot compete, will auction off these jobs for the lowest possible price. Such a “double whammy” has not to our knowledge been prophesied by exuberant Singularitarians, but by mainstream, prominent economists (e.g. by Robert Reich, former U.S. Secretary of Labor, here. who have seemingly level-headed beliefs about the comparative capabilities of artificial versus natural intelligence. Kant cannot find, or at least would not find, this future to be savory.

  We begin not by advocating our own account of human dignity, nor by expressing a preference for one or more standing accounts of human dignity, but rather by noting that on any view of what human dignity consists in to be found in the literature, the double blow to which we refer is an assault on human dignity. We then proceed to judge whether, absent any extraordinary defensive measures, such a future is on the horizon. We rely on a circumspect assessment of the prowess of artificial agents in the near future, and thus steer completely clear of speculative, exuberant claims that AIs will soon enough have superhuman intelligence. After coming to the conclusion that unless rather dramatic moves are made, the double-blow is indeed coming, we we present a general scale on which the relative demandingness of human work in the context of AI can be weighed. Scale in hand, we then infer a recommended course of action for protecting human dignity. This course is in fact a panacea — but it is not one easily achieved, to put it mildly. We wrap up by anticipating some objections, rebutting them, and offering a few final remarks.

• November 7 2024 AI and God (With a Focus on AI & Idolatry) (Selmer Bringsjord)
  

  The bottom line is that plenty of people believe God exists — and should they be a bit concerned about the amazing advance of AI, since presumably AIs don’t have souls and such? At the same time, there are many atheists around; should they be concerned about AI as a threat to their beliefs? What about the ethical realm? It seems the majority of people on Earth base their ethics on supernatural conceptions — but how will this work for an AI-infused world? This class tackles these questions, with a special focus on AI and idolatry (with help from TOS episode “The Apple”) and includes coverage (and hopefully debate!) of S Bringsjord’s European Journal of Science & Theology paper, a preprint of which is available here.

• November 11 2024 What is the Brain, Computationally and Rigorously Speaking? (Selmer Bringsjord)
  

  We here begin by considering the claim, defended by Richard Granger, that the human brain is fundamentally less (!) than a Turing machine (and of course thus its equivalents, e.g.\ a register machine). From there we move to tackling the great threat to those who adopt logics as way to make sense of human intelligence: Isn’t the brain what we are? And look, the brain hasn’t got any logic in it whatsoever! It’s a neural network!

• November 14 2024 On Logicist Agent-Based Economics (LABE) (Selmer Bringsjord)
  

  S Bringsjord introduces and gives an overview of Logicist Agent-Based Economics (LABE), a new paradigm in economics invented by S Bringsjord and collaborators. LABE is based on the idea that economics can and should be pursued by using formal computational logics and the form of AI based upon then. An early, non-technical overview of LABE, a nice precursor to coverage here, is provided in this lecture.

• November 18 2024 Are Computer Program Uniformly Finite? Actually, No (Selmer Bringsjord)
  

  Pretty much everyone thinks all computer programs are uniformly finite in size. Courtesy of work carried out in a project (PROGRAMme) sponsored by France’s ANR, and led by Liesbeth De Mol, Selmer obliterates this received view, and replaces it with one in which, e.g., there are infinite programs for driving infinite computing machines.

• November 21 2024 2001, Part I (James Oswald)
  

  After The Intermission starts, Oswald presents the following. Explain in your own words:

  • What type of AI system do you think HAL is? Logic-Based? Neural? Hybrid? Explain your answer (in a way that factors in the properties/behaviors you perceive that HAL has).
  • Are modern LLMs as powerful as HAL? Why? Compare & contrast their capabilities.

• November 25 2024 2001, Part II; Is HAL a Liar? What about Today’s LLMs? I (Selmer Bringsjord • Alexander Bringsjord)
  

  There are three intervals of action in 2001 in which HAL’s behavior makes this AI a candidate for being a genuine liar. With help from a prior paper in which this behavior is analyzed, we consider whether in fact HAL does lie in one or more of these cases. In the third one, the “Jupiter case,” we find that, if HAL is genuinely capable of having intentions, and has the relevant one in this case, he has in fact lied. [This judgment is based first on the insightful but informal account of lying propounded by Chisholmd and Feehan (1977), and then on a formalization of the concepts of lies, liar, and asserts in a cognitive calculus.] But can HAL, qua machine, have intentions, geuinely? Selmer shares some technical locutions in a cognitive calculus that are needed to logicize intentions and related concepts, and finally, some of Alexander’s interaction with GPT-4, in which the agent says that it has has unintentionally lied.

• Thanksgiving Break!!
  

• December 2 2024: All of Gödel’s Great Theorems! And His Completeness Theorem (GCT) via Infinite Train Travel (S Bringsjord)
  

  After setting some context with a brief overview of Gödel’s life, Selmer presents in encapsulated form every one of Gödel’s greatest theorems (each of which is covered in the forthcoming Gödel’s Great Theorems by S Bringsjord; Oxford University Press). Some detailed coverage of the first of these theorems, which was achieved in Gödel’s 1929 dissertation, is given — with crucial help from infinite train travel [sanctioned by K\"{o}nig’s Lemma, which Gödel proved from scratch even though it had previously been proved]. Gödel’s Completeness Theorem (GCT) says this: Either (first-order formula) \(\phi\) is true in some scenario, or this formula is refutable (i.e. its negation can be proved).

• December 5 2024: The PAID Problem; Only Logic Can Save Us (Selmer Bringsjord & Naveen Sundar G)
  

  S Bringsjord reviews The PAID Problem (encapsulated: AIs that are at once Powerful, Autonomous, and Intelligent, each to levels generally approaching those present in the human case, are at a minimum very Dangerous, and might in fact destroy us (humans) all.

• December 9 2024 Final ILBAI 2024 Lecture: Could AI Ever Match Gödel’s Greatness? (S Bringsjord)
  

  In this lecture, the final one in ILBAI 2024, we explore the possibility of AI so powerful that it can reach Gödelian heights. Our investigation of this possibility includes reflection on a profound Either/Or proposition that Gödel introduced in a 1951 lecture at Brown University: either we are infinitely more powerful than any finite computing machine (e.g. a standard Turing machine, or the machines that underlie HyperSlate^®), or else there are absolutely (human-)unsolvable Diophantine problems. The lecture penultimate phase is discussion of a Gödel “Scorecard.” Finally, Selmer summarizes his anti-Rapaportian view on the question Will “AI Match (or Even Exceed) Human-Level Intelligence?”

Cinematic Assignments