Matteo Pascucci

In this paper we present an approach to conditional reasoning tasks based on two main ideas. The first idea is that, in contrast with what is usually assumed, an ‘if… then…’ sentence is not an adequate translation in natural language of a logical formula containing a material implication as its principal operator. The second idea is that when subjects are required to check the validity of a sentence in a task, their inferences are not driven uniquely by the content of the sentence, but also by other information embedded in the task scenario and, eventually, by their knowledge about the topic (i.e. information stored in memory). Data from 30 subjects tested on six different tasks are reported as evidence for our approach. The results show that conditional tasks are significantly more complex only when they are presented with ‘if… then…’ sentences and when the subject cannot rely on any extra information, such as contextual information or knowledge about the topic.

The present article is devoted to a logical treatment of some fundamental concepts involved in responsibility attribution. We specify a theoretical framework based on a language of temporal deontic logic with agent-relative operators for deliberate causal contribution. The framework is endowed with a procedure to solve normative conflicts which arise from the assessment of different normative sources. We provide a characterization result for a basic system within this framework and illustrate how the concepts formalized can be put at work in the analysis of examples of legal reasoning.

The Mīmāṃsā school of Indian philosophy has for its main purpose the interpretation of injunctions that are found in a set of sacred texts, the Vedas. In their works, Mīmāṃsā authors provide some of the most detailed and systematic examinations available anywhere of statements with a deontic force; however, their considerations have generally not been registered outside of Indological scholarship. In the present article we analyze the Mīmāṃsā theory of Vedic injunctions from a logical and philosophical point of view. The theory at issue can be regarded as a system of reasoning based on certain fundamental principles, such as the distinction between strong and weak duties, and on a taxonomy of ritual actions. We start by reconstructing the conceptual framework of the theory and then move to a formalization of its core aspects. Our contribution represents a new perspective to study Mīmāṃsā and outlines its relevance, in general, for deontic reasoning.

This article concerns the treatment of propositional quantification in a framework of labelled natural deduction for modal logic developed by Basin, Matthews and Viganò. We provide a detailed analysis of a basic calculus that can be used for a proof-theoretic rendering of minimal normal multimodal systems with quantification over stable domains of propositions. Furthermore, we consider variations of the basic calculus obtained via relational theories and domain theories allowing for quantification over possibly unstable domains of propositions. The main result of the article is that fragments of the labelled calculi not exploiting reductio ad absurdum enjoy the Church–Rosser property and the strong normalization property; such result is obtained by combining Girard’s method of reducibility candidates and labelled languages of lambda calculus codifying the structure of modal proofs.

The deontic status of tautologies and contradictions is one of the major puzzles for authors of early works on deontic logic. It is well-known that von Wright addresses this problem by adopting a Principle of Deontic Contingency, which says that tautologies are not necessarily obligatory and contradictions are not necessarily forbidden. A more radical solution is proposed by Anderson within a reductionist approach to deontic logic and consists in restricting the range of application of deontic modalities to contingent propositions. Anderson’s solution has not received much attention in the literature, despite reflecting a typical feature of ordinary deontic reasoning, where non-contingent propositions are rarely, if ever, taken into account. In the present article we explore some of its formal consequences, providing a taxonomy of the properties of the Andersonian operators of obligation and permission for contingent propositions, O′ and P′, in the class of normal alethic systems.

This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named C_t, whose language includes a propositional constant and prove that (I) C_t is complete with respect to a certain class of general frames and (II) the usual operators for past and future necessity are definable in such system. Furthermore, we will introduce the extension C_t(lin) that can be interpreted on linear and transitive general frames. The theoretical result of the current work is that contingency can be treated as a primitive notion in reasoning about temporal modalities.

This article concerns the metatheory of a class of modal logics whose language includes propositional constants of various kinds. The main novelties are the use of general frames with specific restrictions and the definition of the strict range of a formula. Many examples from the literature are treated within the framework provided and some traditional model-theoretic issues such as preservation results concerning the validity of formulas and definability results concerning frame properties are addressed.