A sentence is a line in Aris. A sentence always consists of a text entry,
a line number, and an evaluation value.
Premise
A premise is a sentence that is given. A premise has no rule associated
with it, nor does it have an evaluation value, unless there is an error
in it.
Conclusion
A conclusion is a sentence that is derived from a combination of other
sentences and a rule. A focused conclusion will be highlighted in cyan.
A conclusion has a set of references associated with it.
Goal
A goal is a sentence that the user is looking to meet in a certain proof. The goal window contains all of these sentences, and can be toggled by the key combination CTRL+L (see Keyboard Shortcuts). When a sentence in the proof matches a goal, the proof sentence's line number is highlighted in red, while the goal's line number is changed to match the proof sentence's line number.
Proof
A proof is a set of sentences, beginning with a set of premises and ending with a set of conclusions, that the user is trying to derive something from. The proof window is the main window that appears when the user opens up a proof.
Subproof
A proof within a proof.
Rules
The rules in Aris are a combination of inference rules, equivalence rules, and predicate rules that the user can use to derive sentences. The rules window (also referred to as the rules tablet) is shared amongst all of the proofs in Aris. It can be toggled by the key combination CTRL+R (see Keyboard Shortcuts) from any proof window. For the list of rules, Rules Index.
Evaluation Value
An evaluation value is the value that appears to the right of a sentence's text entry. It can either be ‘’, ‘T’, ‘F’, ‘*’, ‘#’, or ‘?’. ‘’ means that the sentence is awaiting evaluation, except in the case of premises, where this could also mean that there are no errors with it. ‘T’ means that either the conclusion logically follows from its references and rule, or that the goal has been found in the corresponding proof. ‘F’ means that either the conclusion does not logically follow from its references and rule, or that the goal has not been found in the corresponding proof. ‘*’ means that there is a text error with this sentence. ‘?’ means that one of the conclusion's references has a text error. ‘#’ means that the conclusion is missing a rule.
Evaluate
To evaluate a sentence means different things depending on the type of sentence. At the very least, evaluation checks the sentence for text errors, i.e. mis-matched parenthesis, etc. Evaluating a conclusion checks that the sentence's text logically follows from the given references and its rule. Evaluating a goal means checking the corresponding proof for a sentence with this exact same text. To evaluate a sentence use the key combination CTRL+E (see Keyboard Shortcuts).
Reference
A reference is a sentence that is being used to derive a conclusion. A reference is highlighted in violet, and can be added or removed from the current sentence by holding down CTRL, and left-clicking on the desired reference.
Connective
A connective is a logical symbol that connects one or more sentences. The connectives used in system psi are conjuction (^), disjunction (v), negation, (-), conditional (→), and biconditional (<->). In addition, system psi recognizes the one-place connectives of the tautology (T) and the contradiction (!).
Quantifier
A quantifier is thing that does stuff. The quantifiers used in system psi are universal (V), and existential (3).
Conjunction
A conjunction is a connective that connects two or more sentences, denoted by ‘^’. A conjunction claims that ‘sentence a and sentence b’ is a new sentence. A conjunction can be inserted in Aris using the key combination CTRL+7 (see Keyboard Shortcuts).
Disjunction
A disjunction is a connective that connects two or more sentences, denoted by ‘v’. A disjunction claims that ‘sentence a or sentence b’ is a new sentence. A disjunction can be inserted in Aris using the key combination CTRL+\ (see Keyboard Shortcuts).
Negation
A negation is a connective that is inserted in front of a sentence, denoted by ‘-’. A neagion claims that the opposite of the negation is true. A negation can be inserted into Aris using the key combination CTRL+` (see Keyboard Shortcuts).
Conditional
A conditional is a connective that connects two sentences, denoted by ‘→’. A conditional claims that ‘if sentence a, then sentence b’ is a new sentence. A conditional can be inserted in Aris using the key combination CTRL+4 (see Keyboard Shortcuts).
Biconditional
A biconditional is a connective that connects two sentences, denoted by ‘<->’. A biconditional claims that ‘sentence a if and only if sentence b’ is a new sentence. A biconditional can be inserted in Aris using the key combination CTRL+5 (see Keyboard Shortcuts).