Joke Meheus

This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far as it is based on logic. Later, this belief came under attack and logic was deemed inadequate to explicate actual cases of human reasoning. Today, there is a growing interest in reconnecting logic, reasoning and rationality. A central motor for this change was the development of non-classical logics and non-classical formal frameworks. The book contains contributions in various non-classical formal frameworks, case studies that enhance our apprehension of concrete reasoning patterns, and studies of the philosophical implications for our understanding of the notions of rationality.

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM c (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support.

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of the standard worlds-models is characteristic for S5

For centuries, inconsistencies were seen as a hindrance to good reasoning, and their role in the sciences was ignored. In recent years, however, logicians as well as philosophers and historians have showed a growing interest in the matter. Central to this change were the advent of paraconsistent logics, the shift in attention from finished theories to construction processes, and the recognition that most scientific theories were at some point either internally inconsistent or incompatible with other accepted findings. The new interest gave rise to important questions. How is `logical anarchy' avoided? Is it ever rational to accept an inconsistent theory? In what sense, if any, can inconsistent theories be considered as true? The present collection of papers is the first to deal with this kind of questions. It contains case studies as well as philosophical analyses, and presents an excellent overview of the different approaches in the domain.

This paper answers the philosophical contentions defended in Horsten and Welch (2007, Synthese, 158, 41–60). It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we encountered in Aliseda’s algorithms.

In this paper, I present the discussive adaptive logic DLI r . As is the case for other discussive logics, the intended application context of DLI r is the interpretation of discussions. What is new about the system is that it does not lead to explosion when some of the premises are self-contradictory. It is argued that this is important in view of the fact that human reasoners are not logically omniscient, and hence, that it may not be evident to discover the inconsistencies in one's beliefs. In addition to this, DLI r can handle cases in which different participants contradict each other. It is shown that, in both kinds of cases, DLI r leads to an interpretation of the discussion that is as rich as possible (even though no discussive connectives are introduced).

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we encountered in Aliseda’s algorithms

We present the inconsistency-adaptive deontic logic DP r , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r