Translations

the Translate class indicates that a code block will contain translation exercises that require symbolizing natural language sentences.

Propositional Logic

You can create propositional logic translation problems by also adding the class Prop, like so:

~~~{.Translate .Prop}
3.1 P/\Q : People want to know what's going on and questions are unavoidable
~~~

The number 3.1 indicates the exercise number, and the colon separates the solution from the text that will be presented for translation. The result of the above is:

To complete it, replace the text to the left of the submit solution button with your translation, press return to check, and then press "Submit Solution". Propositional translations are considered correct if they are logically equivalent to the original answer. So for example, Q/\P will be accepted above.

First-Order Translation

It is also possible to create first-order translation problems using the class FOL, thus:

~~~{.Translate .FOL}
3.2 AxF(x) : Everything is fine
~~~

with the result:

These are completed as above. Equivalence of first-order sentences is undecidable, so we can't check it, but we can catch most cases of "equivalent" translations by using some rewriting rules.¹ So, for example ~Ex~F(x) will be accepted above.

Exact Translations

Using the class Exact, you can also create "translations" that don't accept logically equivalent answers. These may be useful if you wish to, for example, ask a student what the missing premise in some inference is. So, for example you might write

~~~{.Translate .Exact}
3.3 P : To make a modus ponens inference with P→Q, you need:
~~~

to generate:

Exact translations use the same syntax as Prop by default, but can be configured to use a large number of alternative syntaxes (see below)

Systems

The way that formulas are parsed can also be customized. This is done by setting the system attribute to indicate which formal system you are drawing your syntax from. So for example,

~~~{.Translate .FOL system="magnusQL"}
3.5 AxBx : Everything is bananas
~~~

will generate:

For first-order translations, the available systems are: firstOrder montagueQC magnusQL thomasBolducAndZachFOL thomasBolducAndZachFOL2019 LogicBookPD LogicBookPDPlus hausmanPL howardSnyderPL ichikawaJenkinsQL hardegreePL goldfarbAltND goldfarbNDPlus and goldfarbAltNDPlus.

For propositional translations, the available systems are: prop montagueSC LogicBookSD LogicBookSDPlus hausmanSL howardSnyderSL ichikawaJenkinsSL hausmanSL magnusSL magnusSLPlus thomasBolducAndZachTFL thomasBolducAndZachTFL2019 tomassiPL and hardegreeSL.

For exact translations, the available systems are all of the above, together with modal logic systems .HardegreeSL .HardegreePL .HardegreeWTL, .HardegreeL .HardegreeK .HardegreeT .HardegreeB .HardegreeD .Hardegree4 .Hardegree5, second order systems .SecondOrder .PolySecondOrder, and set theory systems ElementaryST and SeparativeST

Advanced usage

Multiple Solutions

If you wish to allow students to find one translation of a sentence that admits several formalizations, you can use a comma-separated list of admissible solutions. So,

~~~{.Translate .FOL}
3.4 (P /\ Q) \/ R, P/\(Q\/R) : Jack jumped the fence and was caught by the watchman or got away.
~~~

generates

Options and Attributes

In addition to allowing for custom point values with points=VALUE, and turning off submission with submission="none", translations also have the following options

These can be included in the space separated list supplied to the options attribute.

Translation tests

Finally, you can impose one or more extra tests on a translation. This is done by setting the tests attribute to indicate which tests you wish to require the translation to pass. The available tests for propositional translations are

The available tests for first-order translations are all the propositional tests, plus:

When using multiple tests, their names must be separated by spaces, so for example,

~~~{.Translate .FOL tests="PNF maxNeg:0"}
3.6 ~Ex~F(x) : Nothing is not bananas.
~~~

will generate:

Partial Solutions

It's possible to include a partial solution to a translation problem, by including the partial solution after a | following the problem. So for example,

~~~{.Translate .FOL options="nocheck"}
3.7 AxF(x) : Everything is fine
| For all x, x is fine
~~~

Generates