Using interrogative logic to teach classical logic (original) (raw)

Methodological Issues for the Logic of Questions and Commands

International Journal of Cognitive Informatics and Natural Intelligence, 2012

There has been much recent interest in logics for questions and commands. The authors approve, but they argue that methodological issues must be addressed, before it is possible to understand what such logics are for and what they should be like. In particular, the authors deny that the formulas in such logics correspond directly to sentences in ordinary language. Logic is not linguistics. What then are the semantics for the formulas of logics of questions and commands? The focus here is mostly on questions. The authors argue that logics designed to capture the conditions for correct reasoning involving questions require a semantics that treats question-answer pairs as values. They also argue that formal dialogue approaches to the logic of questions should be interpreted in the light of the denial that logic is about language.

Foundations for the Logic of Questions and Commands

Advances in information quality and management, 2014

Recent interest in logics for questions and commands has been prompted partly by a recognition that reasoned argument often involves moves that are not truth-evaluable, and partly by the use of questions and commands in most procedural programming. The authors argue that certain methodological issues must be addressed before we can agree on the purpose and nature of logics for questions and commands. They deny that formulas in such logics should correspond to sentences in ordinary language. They consider how formulas should be interpreted, focusing especially on questions. The authors argue that logics designed to capture the conditions for correct reasoning involving questions require a semantics that treats question-answer pairs as values. This emphasis brings to the fore issues about questions in premise-conclusion arguments. In both premise-conclusion and dialogical argumentation, the authors argue that logic should aim to capture moves in reasoning, not facts about sentences.

On the semantics and logic of declaratives and interrogatives

Synthese, 2013

In many natural languages, there are clear syntactic and/or intonational differences between declarative sentences, which are primarily used to provide information, and interrogative sentences, which are primarily used to request information. Most logical frameworks restrict their attention to the former. Those that are concerned with both usually assume a logical language that makes a clear syntactic distinction between declaratives and interrogatives, and usually assign different types of semantic values to these two types of sentences. A different approach has been taken in recent work on inquisitive semantics. This approach does not take the basic syntactic distinction between declaratives and interrogatives as its starting point, but rather a new notion of meaning that captures both informative and inquisitive content in an integrated way. The standard way to treat the logical connectives in this approach is to associate them with the basic algebraic operations on these new types of meanings. For instance, conjunction and disjunction are treated as meet and join operators, just as in classical logic. This gives rise to a hybrid system, where sentences can be both informative and inquisitive at the same time, and there is no clearcut division between declaratives and interrogatives. It may seem that these two general approaches in the existing literature are quite incompatible. The main aim of this paper is to show that this is not the case. We develop an inquisitive semantics for a logical language that has a clearcut division between declaratives and interrogatives. We show that this

A Uniform Semantics for Embedded Interrogatives: An answer, not necesarily the answer

Our paper addresses the following question: is there a general characterization, for all predicates P that take both declarative and interrogative complements (responsive predicates in Lahiri's 2002 typology), of the meaning of the P-interrogative clause construction in terms of the meaning of the P-declarative clause construction? On our account, if P is a reponsive predicate and Q a question embedded under P, then the meaning of 'P+Q' is, informally, "to be in the relation expressed by P to some potential complete answer to Q". We show that this rule allows us to derive veridical and non-veridical readings of embedded questions, depending on whether the embedding verb is veridical, and provide novel empirical evidence supporting the generalization. We then enrich our basic proposal to account for the presuppositions induced by the embedding verbs, as well as for the generation of weakly exhaustive readings of embedded questions (in particular after surprise).

A multi-type display calculus for inquisitive logic

In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subfor-mula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework developed by Groenendijk, Roelofsen and Ciardelli which captures both assertions and questions in natural language. Inquisitive logic adopts the so-called support semantics (also known as team semantics). The Hilbert-style presentation of inquisitive logic is not closed under uniform substitution, and some axioms are sound only for a certain subclass of formulas, called flat formulas. This and other features make the quest for analytic calculi for this logic not straightforward. We develop a certain algebraic and order-theoretic analysis of the team semantics, which provides the guidelines for the design of a multi-type environment accounting for two domains of interpretation, for flat and for general formulas, as well as for their interaction. This multi-type environment in its turn provides the semantic environment for the multi-type calculus for inquisitive logic we introduce in this paper. Acknowledgements.

Natural Logic for Natural Language

Logic, Language, and Computation, 2007

For a cognitive account of reasoning it is useful to factor out the syntactic aspect-the aspect that has to do with pattern matching and simple substitution-from the rest. The calculus of monotonicity, alias the calculus of natural logic, does precisely this, for it is a calculus of appropriate substitutions at marked positions in syntactic structures. We first introduce the semantic and the syntactic sides of monotonicity reasoning or 'natural logic', and propose an improvement to the syntactic monotonicity calculus, in the form of an improved algorithm for monotonicity marking. Next, we focus on the role of monotonicity in syllogistic reasoning. In particular, we show how the syllogistic inference rules (for traditional syllogistics, but also for a broader class of quantifiers) can be decomposed in a monotonicity component, an argument swap component, and an existential import component. Finally, we connect the decomposition of syllogistics to the doctrine of distribution.

Language, Form, and Logic In Pursuit of Natural Logic's Holy Grail

Oxford University Press, 2023

This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and %Zivanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena.