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Unformatted text preview: are appropriate for making genuine claims about the world.
These are called sentences. Sentences are wﬀs with no free variables. You will learn about these concepts in the text.
To see if what you have written in the sentence window is a sentence, and if so, whether it is true in the world currently displayed,
click on the Verify button in the toolbar. This is the leftmost of the
group of three colored buttons on the toolbar. Alternatively, you Using Tarski’s World / 25 can type Command-Return (Control-Enter on Windows). If you
want to check a whole list of sentences, choose Verify All Sentences from the Sentence menu. Alternatively, use the Verify
All button on the tool bar, which is in the center of the group..
When you verify a sentence, the results are displayed in the
margin to the left of the sentence number: “T” or “F” indicates
that the sentence is true or false in the world, “∗” indicates that
the formula is not well-formed or not a sentence, while “+” indicates that the formula is a sentence of ﬁrst-order logic, but not
evaluable in the current world. When you enter something that
is not well-formed, Tarski’s World will display the portion of the
expression after the error in red. If you are unsure why a sentence
is not evaluable, verifying the sentence again will result in a dialog
explaining the reason.
The evaluations are removed when the sentence or world is
changed. 3.5 Playing the game When you stake out a claim about a world with a complex sentence,
you are committed not only to the truth of that sentence, but also
to claims about its component sentences. For example, if you are
committed to the truth of a conjunction A ∧ B (read “A and B”)
then you are also committed both to the truth of A and to the truth
of B. Similarly, if you are committed to the truth of the negation
¬A (read “not A”), then you are committed to the falsity of A.
This simple observation allows us to play a game that reduces
complex commitments to more basic commitments. The latter
claims are generally easier to evaluate. The rules of the game are
part of what you will learn in the body of this book. Here, we will
explain the kinds of moves you will make in playing the game.
To play the game, you need a guess about the truth value of
the current sentence in the current world. This guess is your initial
commitment. The game is of most value when this commitment is
wrong, even though you won’t be able to win in this case.
Clicking on the Game button, the rightmost of the group of
three colored buttons on the toolbar, will start the game. Tarski’s
World will begin by asking you to indicate your initial commitment.
At this point, how the game proceeds depends on both the form 26 / LPL Software Manual of the sentence and your current commitment. A summary of the
rules can be found in Table 9.1 in Chapter 9 of the textbook. 3.5.1 Picking blocks and sentences As you see from the game rules, at certain points you will be asked
to pick one sentence from a list of sentences. You do this by clicking
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This document was uploaded on 01/26/2014.
- Winter '14