Introduction to (Formal) Logic (via, and also to, AI)

Table of Contents

Selmer Bringsjord
with Naveen Sundar G.
\(\wedge\) Joshua Taylor \(\wedge\) \(\ldots\)

logic_universe.jpg

Larry_by_Kath_v2.jpg

Figure 2: Larry

Lucy_by_Kath_v2.jpg

Figure 3: Lucy

[All artwork (all of which is copyrighted) for the LAMA paradigm by KB Foushee.]

Terminology & General Orientation

This course is an advanced, accelerated introduction to deductive formal logic, with at least some informative pointers to inductive formal logic, in which formalisms for dealing with uncertainty (e.g. probability theory) are included, and to heterogeneous formal logic (which allows reasoning over visual content) as well. This course makes crucial use of AI for learning, and also provides an introduction to AI itself, at least AI of the logicist variety. In particular, students are exposed to a pure and general form of logic programming (so-called PGLP).

Texts/Readings

Students will purchase access to and obtain the inseperably interconnected trio of

  1. the e-text Logic: A Modern Approach; Beginning Deductive Logic via HyperSlatee\(^{TM}\), Advanced (LAMA-BDLA);
  2. the HyperSlate\(^{TM}\) software system for (among other things) proof construction in collaboration with AI technology; and
  3. HyperGrader\(^{TM}\), an AI-infused online system for assessing student progress.

Each member of this trio will be available online after purchase of the relevant code-carrying envelope in the RPI Bookstore. Full logistics of this purchase, and the content of the envelope and how to proceed from this content, will be explained the first class (and subsequently, as needed). Updates to LAMA-BDLA, and additional exercises, will be provided by listing on relevant LAMAe\(^{TM}\) web pages upon signing in (and sometimes by email) through the course of the semester. You will need to manage many electronic files in the course of this course, and e-housekeeping and e-orderliness are of paramount importance. You will specifically need to assemble a library of completed and partially completed proofs so that you can use them as building blocks in harder proofs; in other words, building up your own “logical library” will be crucial.

Please note that HyperSlatee\(^{TM}\) and Slatee\(^{TM}\) are each copyrighted: copying and/or distributing this software to others is strictly prohibited. You will need to AGRRE online after are the time of registration a License Agreement. This agreement will also cover the textbook, which is copyrighted as well, and cannot be copied or distributed in any way, even in part.

In addition, occasionally papers may be assigned as reading. Two, indeed, were assigned in the syllabus, on the first day of class.

Finally, slide decks used in class will contain crucial additional content above and beyond LAMA-BDLA, information posted on HyperGrader\(^{TM}\), and HyperSlate\(^{TM}\); this additional content will be available on the web site as the course unfolds through time.

Syllabi

The version of the course now underway is the Spring 2019 edition, the syllabus for which is available here. This is a robust, detailed syllabus, and is required reading — and reading that will pay off, for sure. Syllabi for some prior years are given in this enumeration:

  • The syllabus for Spring 2018 is available here.
  • You can find the Spring 2017 syllabus, as a pdf, here.
  • The (rather obsolete) Spring 2016 version of the syllabus, as a pdf, is given here.

HyperSlate\(^{TM}\)

This is the software system used for constructing proofs and arguments in collaboration with AI technology, and is available here after registration and sign-in. The older, locally-run-only Slatee\(^{TM}\) system will also be available for those who care to explore it.

HyperGrader\(^{TM}\)

This is the AI system for submitting, getting assessed, and earning points for proofs and arguments constructed in HyperSlate\(^{TM}\) (and Slatee\(^{TM}\)), and is available here after registration and by sign-in.

LAMA-BDLA Textbook

This is the textbook for the course, and is obtained after registration and sign-in, by downloading.

Class-Day Topic and Content (includes associated files; e.g., slide decks, lectures, tutorials, HyperSlate\(^{TM}\) files, etc.)

Homeworks

Homework consists of solving all required problems listed on HyperGrader\(^{TM}\)’s RPI web page. (Non-required problems are clearly marked as such, e.g. as Bonus Problems.) All solutions are created in their final form in HyperSlatee\(^{TM}\). HyperGrader\(^{TM}\) for interactive use via its underlying AI technology opens for its Spring 2019 stint on or about Jan 28 2019, and an orientation/introduction to the system is given in class that day. Note that homeworks cannot be done without access to, and sustained and continuous use of, HyperSlatee\(^{TM}\) and HyperGradere\(^{TM}\).

Footnotes:

1

Warning: Increasingly, the term ‘reasoning’ is used by some who don’t really do anything related to reasoning, as traditionally understood, to nonetheless label what they do. Fortunately, it’s easy to verify that some reasoning is that which is covered by formal logic: If the reasoning is explicit; links declarative statements or formulae together via explicit, abstract reasoning schemata or rules of inference (giving rise to at least explicit arguments, and often proofs); is surveyable and inspectable, and ultimately machine-checkable; then the reasoning in question is what formal logic is the science and engineering of. (An immediate consequence of the characteristics just listed is that AIs based on artificial neural networks don’t reason, ever.) In order to characterize /in/formal logic, one can remove from the previous sentence the requirements that the links must conform to explicit reasoning schemas or rules of inference, and machine-checkability. It follows that so-called informal logic would revolve around arguments, but not proofs. An excellent overview of informal logic, which will be completely ignored in this class, is provided in “Informal Logic” in the Stanford Encyclopedia of Philosophy. In this article, it’s made clear that, yes, informal logic concentrates on the nature and uses of argument.

Author: Selmer Bringsjord

Created: 2019-03-15 Fri 07:58

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