Classical logic

Argumentation in Artificial Intelligence, 2009

Axioms

Since its inception, logic has studied the acceptable rules of reasoning, the rules that allow us to pass from certain statements, serving as premises or assumptions, to a statement taken as a conclusion [...]

2002

In this paper I argue that the debate over the purported distinction between deductive and inductive arguments can be bypassed because making the distinction is unnecessary for successfully evaluating arguments. I provide a foundation for doing logic that makes no appeal to the distinction and still performs all the relevant tasks required of an analysis of arguments. I also reply to objections to the view that we can dispense with the distinction. Finally, I conclude that the distinction between inductive and deductive arguments is not one of the most important and fundamental ideas in logic, but rather is unnecessary

Informal Logic, 2001

In this paper I argue that the debate over the purported distinction between deductive and inductive arguments can be bypassed because making the distinction is unnecessary for successfully evaluating arguments. I provide a foundation for doing logic that makes no appeal to the distinction and still performs all the relevant tasks required of an analysis of arguments. I also reply to objections to the view that we can dispense with the distinction. Finally, I conclude that the distinction between inductive and deductive arguments is not one of the most important and fundamental ideas in logic, but rather is unnecessary.

1999

There has been an increasing demand of a variety of logical systems, prompted by applications of logic in Al, logic prograrnming and other related areas. Labelled Deductive Systems (LDS)[Gab96] were developed as a flexible methodology to formalize such a kind of complex logical systems. In the last decade, defeasible argumentation [SL92, PV99, Ver96, BDKT97] has proven to be a confluence point for many approaches to formalizing commonsense reasoning.

Xaporia, 2023

As a result of trying to distinguish between what we do not know as humans and what we do know, concepts such as dialectic were formed. On this basis, logic was developed to monitor arguments' validity and provide methods for creating valid complex arguments. This work provides a brief overview of such topics and studies the development of formal logic and its semantics. In doing so, we enter the territory of propositional logic and predicate logic. In the next edition, we will discuss modal logic when we confront the future contingent problem.

arXiv (Cornell University), 2022

Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of premises is said to be "contained" in that set; because of this containment relation, the conclusion would be known from the moment the premises are known. Assuming this, it is problematic to explain how we can gain knowledge by deducing a logical consequence implied in a set of known premises. To address this problem, we offer an alternative account of the epistemic contribution of deduction as the process required to deduce a conclusion or a theorem, understanding such process not only in terms of the number of steps in the derivation but, more importantly, the reason for or justification for every step. That is, we do not know a proposition unless we have a justification or proof to hold that proposition. With this goal in mind, we develop a justification logic system which exhibits the epistemic contribution of a deductive derivation as the resulting justified formula.

The main concern of this paper is to give an account of the nature and fundamental features of formal deductive systems in order to understand, precisely, what Kurt Gödel incompleteness theorems speak about them.

PhD dissertation, 1995

Annals of Mathematics and Artificial Intelligence, 2005

In this paper, we establish a formal semantics for Pollock’s [23] theory of defeasible reasoning. As a notion of argument or argumentation has never been formalised in this theory, it is important that such a formal account be introduced to couple with the algorithmic description of the theory. In particular, it makes Pollock’s theory become more comparable to other related frameworks as shown in the paper. In also enforces a well-defined semantical account for Pollock’s theory of defeasible reasoning based on the argumentation-theoretic approach proposed by Dung and Bondarenko et al. [1,5]. Our formalisation thus enables further studies to the meta-theoretic properties of Pollock’s defeasible reasoning system.