Reasoning about update logic

Logical frameworks for analysing the dynamics of information processing abound [4, 5, 8, 10, 12, 14, 20, 22]. Some of these frameworks focus on the dynamics of the interpretation process, some on the dynamics of the process of drawing inferences, and some do both of these. Formalisms galore, so it is felt that some conceptual streamlining would pay off.This paper is part of a larger scale enterprise to pursue the obvious parallel between information processing and imperative programming. We demonstrate that logical tools from theoretical computer science are relevant for the logic of information flow. More specifically, we show that the perspective of Hoare logic [13, 18] can fruitfully be applied to the conceptual simplification of information flow logics.     

Argument practices

The move to Postmodernism in argumentation is often predicated on the rejection of the formal basis of argument in logic. While this rejection may be justified, and is widely discussed in the literature, the loss of logic creates problems that a Postmodern theory of argument must address without recourse to logic and its attendant modernist assumptions. This essay argues that conceiving of argument in terms ofpractices will address the key problematics of Postmodernism without abandoning those features of argumentation that make it an important social, cultural and political practice. Implications for both theory and pedagogy are discussed.The author would like to acknowledge the invaluable commentary of, and discussions with, John Lyne, Charles Willard, Steven Fuller, and Ed Schiappa.     

Why Logic Doesn‘t Matter in the (Philosophical) Study of Argumentation

Philosophically, the study of argumentation is important because it holds out the prospect of an interpretation of rationality. For this we need to identify a transcendent perspective on the argumentative interaction. We need a normative theory of argumentation that provides an answer to the question: should the hearer accept the argument of the speaker. In this article I argue that formal logic implies a notion of transcendence that is not suitable for the study of argumentation, because, from a logical point of view, argumentation disappears from sight. We should therefore not expect formal logic to provide an interesting interpretation of the rationality intrinsic in argument and discussion.     

A critique of Tversky and Kahneman's distinction between fallacy and misunderstanding

Tversky and Kahneman explain cognitive errors in terms of either misunderstanding or fallacy , but have failed to define these concepts. Therefore, they are unable to derive strict diagnostic criteria for distinguishing between them. The lack of conceptual clarification also has prevented them from recognizing the circular relationship between understanding and logicality. Diagnosis of understanding presupposes logicality, and diagnosis of logicality presupposes understanding. This circularity follows when understanding is defined as grasping what is and is not logically implied by a given expression as intended, and when fallacy is defined as logical error. Alternative definitions are discussed and rejected. Tversky and Kahneman fail to realize that one cannot explain and understand what is genuinely illogical, and that, therefore, errors must always be regarded as failure to understand, that is, as logical inference from erroneous premises.     

On the uses of language in working and idealized logic

The interpretation of discourse covers a continuum with two extremes: on the one hand, a text considered as an ideal, distant object, and on the other hand, a conversation regarded as a real, present event. On the basis of a distinction between relatively context-invariant propositions and relatively context-dependent statements, it is argued that statements in conversational discourse are easier to interpret than statements in texts, whereas only propositions in symbolic logic can be interpreted with exactitude. In the same way, the interpretation of dialogical arguments proceeds more easily than the interpretation of arguments in texts. While dialogical argumentation requires a dialectical approach, textual argumentation necessitates an imaginative reconstruction of the argument. From this it can be concluded that for different sorts of argumentative discourse diverse sorts of interpretative activities have to be used.     

Proto-Semantics for Positive Free Logic

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of non-existing objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non unlike the notion of truth at world found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization).     

Scientific Discovery on Positive Data via Belief Revision

A model of inductive inquiry is defined within a first-order context. Intuitively, the model pictures inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure (the real world) from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revision allows scientists to solve a wide class of problems.     

Varieties of Monadic Heyting Algebras. Part III

This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in detail. In particular, we prove that there exist exactly thirteen critical varieties in (MHA) and that it is decidable whether a given variety of monadic Heyting algebras is finite or not. The representation of (MHA) is also given. All these provide us with a satisfactory insight into (MHA). Since (MHA) is dual to the lattice NExtMIPC of all normal extensions of the intuitionistic modal logic MIPC, we also obtain a clearer picture of the lattice structure of intuitionistic modal logics over MIPC.