If a logic is deductive then it must be sound , i.e. its rules must not not allow a falsehood to be derived from true premises. For this to work reliably you really need a formal language with formally defined logical axioms and inference rules. The permitted inferences are sound . A method of reasoning is non-deductive if, even when correctly followed, it may permit the derivation of a conclusion which is false from premises which are all true, or if the inference rules are not sufficiently definite to settle questions about what can correctly be inferred. The most widely studied form of non-deductive reasoning is probably in ductive reasoning, which has been supposed by many to justify inference to general scientific laws from particular experimental observations.
Induction is neither sound nor definite.
A language is formal if the syntax of the language is defined with sufficient precision that a computer could be programmed to check whether any particular sentence belongs to the language. There are many different kinds of formal notation. Any of these may become part of a formal logic, though few do. A full understanding of the scope of logic depends upon understanding how arbitrary formal notations can be integrated into a logical system. The key aspect of a language which determines whether it can be made into a logic is the definition of the language, which is the primary output from the process of designing a language.