Logical arguments are usually classified as either 'deductive' or 'inductive'.
Deduction: In the process of deduction, you begin with some statements, called 'premises', that are assumed to be true, you then determine what else would have to be true if the premises are true. For example, you can begin by assuming that God exists, and is good, and then determine what would logically follow from such an assumption. You can begin by assuming that if you think, then you must exist, and work from there. In mathematics you can begin with some axioms and then determine what you can prove to be true given those axioms. With deduction you can provide absolute proof of your conclusions, given that your premises are correct. The premises themselves, however, remain unproven and unprovable, they must be accepted on face value, or by faith, or for the purpose of exploration.
Induction: In the process of induction, you begin with some data, and then determine what general conclusion(s) can logically be derived from those data. In other words, you determine what theory or theories could explain the data. For example, you note that the probability of becoming schizophrenic is greatly increased if at least one parent is schizophrenic, and from that you conclude that schizophrenia may be inherited. That is certainly a reasonable hypothesis given the data. Note, however, that induction does not prove that the theory is correct. There are often alternative theories that are also supported by the data. For example, the behavior of the schizophrenic parent may cause the child to be schizophrenic, not the genes. What is important in induction is that the theory does indeed offer a logical explanation of the data. To conclude that the parents have no effect on the schizophrenia of the children is not supportable given the data, and would not be a logical conclusion.
Deduction and induction by themselves are inadequate for a scientific approach. While deduction gives absolute proof, it never makes contact with the real world, there is no place for observation or experimentation, no way to test the validity of the premises. And, while induction is driven by observation, it never approaches actual proof of a theory. The development of the scientific method involved a gradual synthesis of these two logical approaches.
For a more comprehensive discussion of deduction, and induction, read the relevant sections of the book by Copi, referenced on this page.