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We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Explainability of algorithmic decision-making systems is both a regulatory objective and an area of intense research. The article argues that a crucial condition for the acceptability of algorithmic decision-making systems is that decisions…
In order to enrich dynamic semantic theories with a `pragmatic' capacity, we combine dynamic and nonmonotonic (preferential) logics in a modal logic setting. We extend a fragment of Van Benthem and De Rijke's dynamic modal logic with…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
The aim of this paper is to propose a many-valued modal framework to formalize reasoning with both graded preferences and propositions, in the style of van Benthem et al.'s classical modal logics for preferences. To do so, we start from Bou…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
We extend the $ASPIC^+$ framework for structured argumentation so as to allow applications of the reasoning by cases inference scheme for defeasible arguments. Given an argument with conclusion `$A$ or $B$', an argument based on $A$ with…
Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. While the usual implication (i.e., the neck of a Horn clause) stands for…
We introduce the operation of possibility qualification and show how. this modal-like operator can be used to represent "typical" or default knowledge in a theory of nonmonotonic reasoning. We investigate the representational power of this…
In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
There are several contexts of non-monotonic reasoning where a priority between rules is established whose purpose is preventing conflicts. One formalism that has been widely employed for non-monotonic reasoning is the sceptical one known as…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…