anita 0.1.7

ANITA is a proof assistant for teaching analytic tableaux to computer science students. ANITA allows students to write their proofs and automatically checks whether the proofs are correct and, if not, displays any errors found.

Analytic Tableau Proof Assistant (ANITA)

The ANITA is a tool written in Python that can be used in desktop, or in a web platform. The main idea is that the students can write their proofs as similar as possible to what is available in the textbooks and to what the students would usually write on paper. ANITA allows the students to automatically check whether a proof in the analytic tableaux is valid. If the proof is not correct, ANITA will display the errors of the proof. So, the students may make mistakes and learn from the errors. The web interface is very easy-to-use and has:

• An area for editing the proof in plain text. The students should write a proof in the Fitch-style.
• A message area to display whether the proof is valid, the countermodel, or the errors on the proof.
• And the following links:
  • Check, to check the correctness of the proof;
  • Manual, to view a document with the inference rules and examples;
  • LaTeX, to generate the LaTeX code of the trees from a valid proof. Use the qtree package in your LaTeX code;
  • LaTeX in Overleaf, to open the proof source code directly in Overleaf that is a collaborative platform for editing LaTeX

To facilitate the writing of the proofs, we made the following conventions in ANITA:

• The Atoms are written in capital letters (e.g. A, B, H(x));
• Variables are written with the first letter in lowercase, followed by letters and numbers (e.g. x, x0, xP0);
• Formulas with $\forall x$ and $\exists x$ are represented by $Ax$ and $Ex$ ('A' and 'E' followed by the variable x). For instance, Ax(H(x)->M(x)) represents $\forall x~(H(x)\rightarrow M(x))$.
• Table below shows the equivalence of logic symbols and those used in ANITA.
• The order of precedence of quantifiers and logical connectives is defined by $\lnot,\forall,\exists,\wedge,\vee,\rightarrow$ with right alignment. For example:
  • Formula ~A&B -> C represents formula $(((\lnot A)\land B)\rightarrow C)$;
  • The theorem ~A|B |- A->C represents $((\lnot A)\vee B)\vdash (A\rightarrow B)$.
• Each inference rule will be named by its respective connective and the truth value of the signed formula. For example, &T represents the conjunction rule when the formula is true. Optionally, the rule name can be omitted.
• The justifications for the premises and the conclusion use the reserved words pre and conclusion, respectively.

Symbol	$\lnot$	$\land$	$\lor$	$\rightarrow$	$\forall x$	$\exists x$	$\bot$	branch	$\vdash$
LaTeX	$\backslash\textrm{lnot}$	$\backslash\textrm{land}$	$\backslash\textrm{lor}$	$\backslash\textrm{rightarrow}$	$\backslash\textrm{forall x}$	$\backslash\textrm{exists x}$	$\backslash\textrm{bot}$	$[.~]$	$\backslash\textrm{vdash}$
ANITA	~	&	$\mid$	->	Ax	Ex	@	{ }	|-

License

ANITA is avalible by a MIT License. Copyright (c) 2022-2022 Davi Romero de Vasconcelos

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Requirements:

• You must install the rply 0.7.8 package

ANITA in your code

You can import ANITA in your code (basic usage)

from anita.anita_en_fo import check_proof

print(check_proof('''1. T A|B		pre
2. T A->C		pre
3. T B->C		pre
4. F C			conclusion
5. {	T A		1
6.	{	F A	    2
7.		@	    5,6
	}
8.	{	T C	    2
9.		@	    8,4
	}
   }
10.{	T B		1
11.	{	F B	    3
12.		@	    10,11
	}
13.	{	T C 	3
14.		@	    13,4
	}
   }
'''))

A Portuguese Version

We have a portuguese version:

• In ANITA syntax, use conclusaoinstead of conclusion.

• You can import ANITA in your code (basic usage)

from anita.anita_pt_fo import check_proof

print(check_proof('''1. T A|B		pre
2. T A->C		pre
3. T B->C		pre
4. F C			conclusao
5. {	T A		1
6.	{	F A	    2
7.		@	    5,6
	}
8.	{	T C	    2
9.		@	    8,4
	}
   }
10.{	T B		1
11.	{	F B	    3
12.		@	    10,11
	}
13.	{	T C 	3
14.		@	    13,4
	}
   }
'''))