The observational advantages of euler diagrams with existential import

The ability of diagrams to convey information effectively in part comes from their ability to make facts explicit that would otherwise need to be inferred. This type of advantage has often been referred to as a free ride and was deemed to occur only when a diagram was obtained by translating a symbolic representation of information. Recent work gen- eralised free rides to the idea of an observational advantage, where the existence of such a translation is not required. Roughly speaking, it has been shown that Euler diagrams without existential import are observa- tionally complete as compared to symbolic set theory. In this paper, we explore to what extent Euler diagrams with existential import are ob- servationally complete with respect to set-theoretic sentences. We show that existential import significantly limits the cases when observational completeness arises, due to the potential for overspecificity

Factivity and presupposition in Dependent Type Semantics

Dependent type theory has been applied to natural language semantics to provide a formally precise and computationally adequate account of dynamic aspects of meaning. One of the frameworks of natural language semantics based on dependent type theory is Dependent Type Semantics (DTS), which focuses on the compositional interpretations of anaphoric expressions. In this paper, we extend the framework of DTS with a mechanism to handle logical entailment and presupposition associated with factive verbs such as know. Using the notion of proof objects as first-class objects, we provide a compositional account of presuppositional inferences triggered by factive verbs. The proposal also gives a formal reconstruction of the type-distinction between propositions and facts, and thereby accounts for the lexical semantic differences between factive and non-factive verbs in a typetheoretical setting

Sequent Calculus for Euler Diagrams

Proof systems play a major role in the formal study of diagrammatic logical systems. Typically, the style of inference is not directly comparable to traditional sentential systems, to study the diagrammatic aspects of inference. In this work, we present a proof system for Euler diagrams with shading in the style of sequent calculus. We prove it to be sound and complete. Furthermore we outline how this system can be extended to incorporate heterogeneous logical descriptions. Finally, we explain how small changes allow for reasoning with intuitionistic logic

An empirical study of diagrammatic inference process by recording the moving operation of diagrams

Inthisstudy,weinvestigatehowpeoplemanipulatediagrams in logical reasoning, especially no valid conclusion (NVC) tasks. In NVC tasks, premises are given and people are asked to judge whether “no consequence can be drawn from the premises.” Here, we introduce a method of asking participants to directly manipulate instances of dia- grammatic objects as a component of inferential processes. We observed how participants move Euler diagrams, presented on a PC monitor, to solve syllogisms with universally quantified sentences. In the NVC tasks, 88.6% of our participants chose to use an enumeration strategy with mul- tiple configurations of conclusion diagrams and/or a partial-overlapping strategy of placing two circles. Our results provide evidence that NVC judgment for tasks with diagrams can be reached using an efficient way of counter-example construction