On Nonfoundational Reasoning

Defeasible reasoning (in short, DR) is indispensable when dealing with a world full of uncertainties: we constantly draw conclusions that we may reject later in view of new information. Examples of DR are numerous: induction, abduction, inferences on the basis of expert opinion, etc. We find DR in everyday reasoning, in expert reasoning (e.g. medical diagnosis), and in scientific reasoning. When reasoning defeasibly, people sometimes make mistakes (they fail to reject conclusions when there are good reasons to do so). Given that DR is central for human reasoning, this urges us to study DR with exact formal methods. Only in this way, are we able to explicate and evaluate reasoning processes in a precise way and to assist and correct people in reasoning. One of the central ideas behind this project is that DR is best studied from an argumentative angle according to which an inference is retracted if and only if it cannot be defended against counterarguments. Besides its technical elegance, it has been argued that the argumentative approach is empirically adequate. Based on Dung's seminal abstract argumentation graphs, several frameworks for DR have been presented. However, there are still many foundational issues and the given tools are still limited in expressive power. DR has also been intensively studied within the domain of nonmonotonic logic, leading to a plethora of logics for different types of DR. What is lacking though, is a formal base that unifies the modeling of various types of DR and that is sufficiently expressive to handle real-life examples of DR. The aim of this project is: (i) to provide a unifying theory for the formal study of DR from an argumentative perspective and (ii) to apply this theory to actual cases of DR. For (i), we will integrate techniques from highly unifying nonmonotonic logics (such as Adaptive Logics) into argumentation frameworks. For (ii), we will focus on two domains: normative reasoning and scientific reasoning.

Artificial Intelligence, 2002

We present different constructions for non-prioritized belief revision, that is, belief changes in which the input sentences are not always accepted. First, we present the concept of explanation in a deductive way. Second, we define multiple revision operators with respect to sets of sentences (representing explanations), giving representation theorems. Finally, we relate the formulated operators with argumentative systems and default reasoning frameworks.

The Southern Journal of Philosophy, 1981

Epistemological Foundationalism is hardly a tenable candidate for the metaphysics of empirical knowledge. Its main alternative is what may be called the Coherence theory of epistemic justification-if one is able to make sense of a theory deserving such a name-and there are reasons for pessimism when one looks at the earlier attempts to clarify, formulate, and apply the alternatives to Foundationalism. However, I take it that my task here is merely to indicate where exactly the primary problem marring Nonfoundationalism might lie. I shall suggest that outside Foundationalism it is difficult, but not impossible, to make sense of the idea that there is any empirical evidence available to a rational epistemic subject and I shall illustrate the problem by means of an example. Nothing else will be attempted. We shall study an epistemological theory which is closely associated with the Coherence theory of truth in its classic idealistic form. The main issues to be dealt with can be illuminated if we focus on this theory: it dismisses exactly what is important in any explication of the necessary conditions of the existence of knowledge. What I mean is that whatever coherence methods we might develop and use in order to be able to make decisions to the effect that one's (empirical) beliefs are justified in certain circumstances or even that these beliefs are true, they must be grounded on some evidence; they must not be outrightly fictional. That there is suitable evidence available for epistemological purposes in the first place is possibly never proved to be true but merely stipulated to be true, presupposed as a methodological necessity or even dismissed as a possible problem (cf. [4], pp. 38-9). But certainly, coherence methods work only if they are applied to some sets of propositions which are iniriullypluusible as to their truth. It is easy to see that one cannot start one's truth-seeking from some pre-established truths, but neither can one start from merely fictional propositions; one therefore starts from potential truths ([7], pp. 50, 54; also [2]). One must be able to make important preliminary decisions here, but on what basis?

Dialogues and Defeasible Reasoning Shahid Rahman (draft 29 April 2011) Abstract: The standard logical approaches to model argumentation forms that involve defeasibility stress either the point on the non monotonic property of the turn-style or introduce a specific conditional (or a combination of the two). In a game-theoretic approach this means that either it is a property of winning strategies or it is about the rules that define a new logical constant (particle rules). In the present paper we will make use of an alternative to the approaches mentioned about available to the dialogical approach. The dialogical approach, as developed in the appendix, distinguishes between • the rules defining the constants (local meaning), • the rules that determine how to play (global meaning) and • the rules that delineate the ways to win (strategic level) if winning is possible • the notion of winning at play level from winning at the strategic level In this context, defeasible reasoning is about introducing some restrictions on the rules on how to play (global meaning), it consists neither in introducing a new conditional (at the local level) nor in changing the winning-strategies. According to our view, defeasibility principle involves semantic features at the global level. More precisely, according to the dialogical approach, defeasibility amounts to the task of verifying that the proponent’s thesis is compatible with the last concession(s) introduced in the play. Notice that the theory of meaning underlying dialogical logic provides a uniform semantics that though it is neither model-theoretic non-proof-theoretic can capture the features of both of those approaches within one frame. Moreover, this approach allows to distinguish John Pollock’s justification of a belief relative to the actual defeasible reasoning at a given stage from warrant which assumes the set of all possible inferences that can be drawn by an idealized player at a given stage. In the dialogical framework, while warrant corresponds to the strategic level (triggered by the extensive form of the play at a given stage) justification corresponds to the play level. Precisely the dialogical level where the semantics is generated and where Pollock’s notion of multiple assignments find its natural place. It should be also pointed out that the dialogical framework provides to the development defeasible reasoning a level beyond the one of play and strategy: the level of cycles linked to the notion of dialogue-defineteness Dialogical defineteness is the dialogical way to deal with Church’s theorem on the non-decidability of first-order logic. The analysis of defeasible reasoning within the dialogical framework should help to build a link between the approaches of default-logic and the argument-based approach initiated by John Pollock [1987], which defines notions like argument, counterargument, attack and defeat, and defines consequence notions in terms of the interaction of arguments for and against certain conclusions.

Non-monotonicity in logic is a symptom that may have many causes. In the formalisation of defeasible reasoning, an epistemic diagnosis has largely prevailed according to which some inferences are non-monotonic because they are provisionally drawn in the absence of relevant or complete information. The Gabbay-Makinson rules for cumulative consequence relations are a paradigmatic example of this epistemic approach. In this paper a different approach to defeasible reasoning is introduced, based on the idea of inferential perspectives. According to this approach, some inferences are non-monotonic because they are drawn as from another reasoner’s perspective. Rules are introduced and discussed for a Perspectival Calculus, which show both similarities and interesting differences with respect to cumulative systems.