REMODEL · Structures for modal and deontic logics

Structures for modal and deontic logics

The aim of the REMODEL project is to provide a logical framework to describe, analyze and explain normative reasoning. At its core, the project is concerned with advancing logical methods for the study of deontic logics—a class of non-classical logics designed to formalize notions such as obligation, permission, and related normative concepts. These systems are useful to represent legal reasoning and ethical dilemmas. From a semantic point of view, they can be grouped in two categories: preference-based systems and norm-based ones. The main technical tool to represent formal reasoning is proof theory. Proof theory, a branch of mathematical logic, investigates the structure of proofs (or derivations) to gain insights into the properties of formal systems. Traditionally, deontic logics are presented using Hilbert-style—or axiomatic—calculi. These systems consist of a set of axioms and a small number of inference rules, offering a compact and elegant formulation of non-classical logics. Moreover, they are modular: new systems can be constructed from base systems by simply adding axioms. However, while axiomatic systems are elegant, they are not well-suited for studying the internal structure of proofs or for practical reasoning tasks, as constructing derivations in them can be particularly challenging. To foster applicability of non-classical logics it is desirable to develop analytic calculi. In contrast to axiomatic calculi, analytic systems allow for a bottom-up analysis of statements or arguments which are decomposed through the rules of the calculus. Therefore, analytic calculi allow for backward reasoning and they are key to design automated proof methods. The most prominent analytic proof methods are sequent calculi and their generalizations. While standard sequent calculi manipulate multisets of formulas, their extensions—such as hypersequents, nested sequents, and labelled sequents—operate on more complex structures like multisets of sequents, trees, or graphs of sequents, respectively. The REMODEL project will provide uniform analytic calculi for deontic logics. A well-designed analytic calculus for deontic logics will be able to perform a twofold task. On the one hand, when a given formula or argument (suitably written in the formal Language) is valid, the calculus must produce a derivation which certifies its validity. On the other hand, whenever it turns out to be false, the calculus has to halt the search for a proof after a finite number of steps and then exhibit a finite countermodel, i.e. a semantic counterexample which gives a reason as to why the formula does not hold. The project will begin by addressing preference-based deontic logics, before moving on to study non-monotonic forms of deontic reasoning. A key methodological approach of REMODEL is the transfer of results from modal logic to deontic logic. This will be achieved by establishing formal translations between the two, thereby creating bridges that allow for the reuse of well-established techniques and results from modal logic. This not only facilitates the development of analytic calculi for deontic logics but also opens up new perspectives in the theory of modal logics themselves.

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