Boolean considerations on John Buridan's octagons of opposition

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework.     

Substitution Logic: An Extension of Syllogism

I examine the theoretical difficulties of Aristotle’s syllogism and the traditional syllogism. I propose a more unified ordinary thinking logic different from the syllogism. I show that the new logic based on the substitution of thinking elements can be used to describe the reasoning process of human minds more properly, bypassing rigid figures, moods and cumbersome rules of the syllogism. I also show that the new logic combines the categorical inference with relation and modal inferences, expanding the scope of the syllogism so that more complex quantification inferences can be captured. I conclude that the substitution of thinking elements is the basic characteristics of human thinking, and the substitutions can be further applied not only to all research fields of abstract and image thinking but also to practical fields of action methodology.     

The Use of Syllogism in Rational-Emotive Therapy

The author indicates how the use of syllogistic logic in rational-emotive therapy can help therapists expose clients' irrational beliefs.     

A Formal Analysis of Relevance

We investigate the notion of relevance as it pertains to ‘commonsense’, subjunctive conditionals. Relevance is taken here as a relation between a property (such as having a broken wing) and a conditional (such as birds typically fly). Specifically, we explore a notion of ‘causative’ relevance, distinct from ‘evidential’ relevance found, for example, in probabilistic approaches. A series of postulates characterising a minimal, parsimonious concept of relevance is developed. Along the way we argue that no purely logical account of relevance (even at the metalevel) is possible. Finally, and with minimal restrictions, an explicit definition that agrees with the postulates is given. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Modal Sortal Logic

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.     

A Modal Logic of Metaphor

The purpose of this paper is to suggest a formal modelling of metaphors as a lingustic tool capable of conveying meanings from one conceptual space to another. This modelling is done within DDL (dynamic doxastic logic).     

A Logical Account of Formal Argumentation

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.     

A Case for Modal Fragmentalism

Philosophia - The idea of fragmentalism has been proposed by Kit Fine as a non-standard view of tense realism. This paper examines a modal version of the view, called modal fragmentalism, which...     

A Model Theory of Modal Reasoning

This paper presents a new theory of modal reasoning, i.e. reasoning about what may or may not be the case, and what must or must not be the case. It postulates that individuals construct models of the premises in which they make explicit only what is true. A conclusion is possible if it holds in at least one model, whereas it is necessary if it holds in all the models. The theory makes three predictions, which are corroborated experimentally. First, conclusions correspond to the true, but not the false, components of possibilities. Second, there is a key interaction: it is easier to infer that a situation is possible as opposed to impossible, whereas it is easier to infer that a situation is not necessary as opposed to necessary. Third, individuals make systematic errors of omission and of commission. We contrast the theory with theories based on formal rules.     

A Modal Logic for Mixed Strategies

Modal logics have proven to be a very successful tool for reasoning about games. However, until now, although logics have been put forward for games in both normal form and games in extensive form, and for games with complete and incomplete information, the focus in the logic community has hitherto been on games with pure strategies. This paper is a first to widen the scope to logics for games that allow mixed strategies. We present a modal logic for games in normal form with mixed strategies, and demonstrate its soundness and strong completeness. Characteristic for our logic is a number of infinite rules.     

A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.     

Formal paraphasias: A single case study

A case study is reported of an aphasic patient, RB, who showed frequent form-related whole-word substitutions in oral naming, writing to dictation, and reading aloud. In both written language tasks, the abstractness of the targets influenced the number of formal errors. In oral naming, a high proportion of formal paraphasias was related to the intended words in both form and meaning. A comparison between targets and formal paraphasias indicated a high agreement both in word class, number of syllables, stress pattern, and in basic (stressed) vowels. The agreement in consonants (including word-initial consonants), however, was low. It is argued that RB's formal substitutions are not caused solely by errors of lexical selection but that semantic, lexical, and segmental factors contribute to the error outcome.     

A New Defence of the Modal Existence Requirement

In this paper, I defend the claim that an object can have a property only if it exists from two arguments, both of which turn on how to understand Plantinga’s notion of the α-transform of a property. For comments and discussion, thanks to David Sanson and three anonymous referees. For funding in the form of a Standard Research Grant (410-2004-0702), thanks to the Social Sciences and Humanities Research Council of Canada (SSHRC).     

A Modal View on Resource-Bounded Propositional Logics

Studia Logica - Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as...