Logic Truth Tree Solver
The Truth Tree Solver is a free-to-use web tool that determines the consistency of a set of logical sentences according to the rules of either Sentential Logic (SL) (aka Propositional Logic or Propositional Calculus) or Predicate Logic (PL). Given a set of symbolic sentences, this tool constructs a truth tree and outputs its visual representation using the same format as in The Logic Book by Bergmann, Moor and Nelson.
You may indeed use this tool as an alternative to the Student Solutions, or even find the solution for problems of the book for which no solution has been provided.
If you are unfamiliar with Logic, or with the truth tree method for determining set consistency, you can try this application anyway by choosing the "Demo!" tab.
If you already know about truth trees and you are dying to find how to use this tool, you may now proceed by clicking on the formal system of your choice (Sentential Logic or Predicate Logic) and following the 3 easy steps.
STEP 1: Compose a sentence
Write a symbolic sentence in the text field below. You may add any letters with your keyboard and add special characters using the appropriate buttons. When your sentence is ready, click the "Add" button to add this sentence to your set. You may add additional sentences to your set by repeating this step.
STEP 2: Validate your set
Ensure that your set contains all and only the sentences you need. You may choose to remove unnecessary sentences by clicking the "Remove" button located on the right of the sentence you want to remove.
Your set contains the following sentences:
STEP 3: Get the result
Finally you can generate a truth tree by clicking the "Generate the tree!" button below. If your can't see the button, it means your set of sentences is empty or that you already generated the tree.
Once the tree is generated, interpret the result. If all terminal nodes end with the cross-symbol (✕), then your set is inconsistent. On the other hand, if there is at least one terminal node without a cross-symbol, then your set is consistent.
STEP 1: Compose a sentence
Write a symbolic sentence in the text field below. You may add any letters with your keyboard and add special characters using the appropriate buttons. When your sentence is ready, click the "Add" button to add this sentence to your set. You may add additional sentences to your set by repeating this step.
STEP 2: Validate your set
Ensure that your set contains all and only the sentences you need. You may choose to remove unnecessary sentences by clicking the "Remove" button located on the right of the sentence you want to remove.
Your set contains the following sentences:
STEP 3: Get the result
Finally you can generate a truth tree by clicking the "Generate the tree!" button below. If your can't see the button, it means your set of sentences is empty or that you already generated the tree.
Once the tree is generated, interpret the result. If all terminal nodes end with the cross-symbol (✕), then your set is inconsistent. On the other hand, if there is at least one terminal node without a cross-symbol, then your set is consistent.
Here are some examples of what kind of visual representations the Truth Tree Solver can generate.
Each gray box represents a set of sentences. The Truth Tree Solver takes as input these sets of sentences and generates a truth tree in the PNG image format.
The first sample set contains a single sentence of Sentential Logic.
Click the "Demo!" button now to see what is generated.
The result should appear in the gray box, below the sentence.
- ∼([(W & Y) ⊃ H] ≡ [W ⊃ (Y ⊃ H)])
The second sample set contains three sentences of Predicate Logic.
Predicate Logic is an extension of Sentential Logic.
Every sentence of SL is also a sentence of PL but the opposite is not true.
In the sample below, all sentences are well formed sentences of PL but they are not well formed sentences of SL because they all contain quantifiers.
- (∀w)∼Gww
- ∼(∀x)Hx ⊃ (∃y)Gya
- ∼(∃z)(Hz & ∼Gzz)
Do you like this app to the point that you would like to help improve it? If so, there are several ways you can do it.
The first and simplest way is to make a donation using PayPal.
Any amount is accepted. Click the "Donate" button below and you will be redirected to the PayPal website.
You will then be prompted to enter the amount you wish to donate as well as your personal information required to process the transaction.
You can choose to specify an improvement that you would like to see implemented and it will be given a higher priority.
However, I reserve my right to ignore the priority if I determine that the amount is considerably insufficient given the requested improvement.
To avoid any confusion, feel free to contact me before making a donation.
Donations are used for paying fees such as translation, graphics design, computer software and hardware or any other expenditure related to developping this application.
The second way to contribute to this application is to buy the book by clicking the top-left Amazon advertisement (the one with the front cover of the book) and I will get a percentage of the sales revenue from Amazon. If you don't see the ad, it's probably because you are using an ad blocker. Turn it off temporarily if you want to buy The Logic Book from this site.
The third way is to report a bug, report a misspelling, make a suggestion, or cheer me up with a good hearted message. Simply go to the contact section of the website and send your comments.
And finally the fourth way is to help translate the Truth Tree Solver in your own native language. Contact me at me@gabriellabrecque.com and tell me what language you would like to translate it to.
