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A syllogism is a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises). It played a crucial role in medieval scholasticism, enabling theologians and philosophers to construct logical arguments for various doctrinal and philosophical issues.

The dialectic method involves the structured exchange of arguments and counter-arguments, sought to uncover truth through dialogue and debate. It was a main feature in medieval education and intellectual endeavors, popularized by figures like Peter Abelard.

Realism is the belief in the independent existence of universals, while nominalism denies their real existence. This distinction was fundamental to medieval philosophical discourse and was a central issue during the Scholastic period.

Universals are the abstract qualities or properties that can be predicated of multiple things. Medieval debate on universals was significant in the development of scholastic philosophy, influencing discussions about the nature of reality and knowledge.

Scholasticism is a medieval school of philosophy that sought to reconcile the philosophy of the ancient classical philosophers with medieval Christian theology. It centered on rigorous dialectical reasoning to understand and explain doctrine.

Inductive reasoning involves making generalizations based on observations and empirical evidence. While less emphasized in medieval thought compared to deduction, it still played a role in the development of scientific and philosophical inquiry.

Analogical reasoning involves inferring that what is true in one case will be true in another similar case. It was commonly used in medieval theological discourse for explaining concepts metaphorically when direct explanations were elusive.

Modus Ponens is a form of argument where from 'If A, then B' and 'A' it follows that 'B'. It was used in medieval logic as a basic and unquestionable form of valid inference, important for constructing theological and philosophical arguments.

Modus Tollens is a form of argument in which from 'If A, then B' and 'Not B' it follows that 'Not A'. It was an essential tool for medieval logicians to dismantle arguments by showing the consequences of a proposition to be false.

Fallacies are mistaken beliefs based on unsound arguments. Medieval logicians, like their ancient predecessors, were keen on identifying fallacies to avoid errors in theological and philosophical reasoning.

Disputation was a formalized method of debate concerning some proposition, where opposing arguments were put forward. This method was integral to medieval academic practice, particularly within universities.

Ockham's Razor is a principle attributed to William of Ockham stating that without sufficient evidence, one should not increase, beyond what is necessary, the number of entities required to explain anything. It emphasized simplicity and parsimony in philosophical and theological explanations.

Abductive reasoning is a form of logical inference which starts with observations and seeks to find the simplest and most likely conclusion. While not formally recognized in medieval logic, its principles resemble methods used to infer explanations for observations.

The Principle of Contradiction states that contradictory statements cannot both be true in the same sense at the same time. Medieval thinkers employed this principle as a fundamental axiom in constructing and evaluating logical arguments.