Using the Carnap site
Explains how instructors set up courses, upload problem sets, assign uploaded problem set or problem sets from the Carnap book them to their courses, and download grades.
Systems supported by Carnap
Describes the syntax, ASCII-only variants of symbols used, and idiosyncrasies of the various systems supported by Carnap. Note: not all of these systems have supported corresponding proof systems.
Carnap supports various kinds of problems, which are described on the following pages:
- Syntax Checking exercises ask students to parse a formula.
- Translation exercises ask students for formulas which Carnap compares to model translations of English sentences. These can also be used for normal forms and equivalences.
- Truth Tables exercises ask students to fill in truth tables and answer questions on the basis of truth tables.
- Derivations exercises asks students to construct proofs in formal systems, which Carnap checks for correctness on-the-fly. Carnap can handle the following systems:
- Montague: Montague-style systems, two of which are used in the Carnap book.
- Logic Book: The Fitch system used in Bergmann, Moore, and Nelson's Logic Book.
- forall x: Fitch system used in Magnus's original forall x.
- forall x: Calgary: Fitch system used in the Calgary version of forall x by Thomas-Bolduc and Zach (and also in Tim Button's forall x: Cambridge.
- Chains of equivalences: a simple proof system where every line results from the previous one by substituting equivalents.
- Fitch-style systems of Gamut's Introduction to Logic.
- Systems based on Howard-Snyder's The Power of Logic.
- Systems based on Hausman's Logic and Philosophy.
- Lemmon-style systems based on Goldfarb's Deductive Logic.
- Lemmon-style system based on Tomassi's Logic
- Hardegree-style systems based on Hardegree's Modal Logic
- Sequent Calculus: Gentzen's sequent systems LK and LJ.
- Gentzen-Prawitz Natural Deduction: Gentzen's original tree-style natural deduction proofs as also used by Prawitz.
- Model Checking asks students to provide first-order interpretations that make given formulas true or false, or show that arguments are invalid.
- Qualitative Problems provide ways for including multiple-choice, multi-select, short answer, and numerical questions on a problem set.
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