Related papers: Proof-Theoretic Semantics, a Problem with Negation…

In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…

We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a…

In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in…

We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…

Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…

Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…

We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…

We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…

A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…

Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…

I discuss two approaches to monotonic proof-theoretic semantics. In the first one, which I call SVA, consequence is understood in terms of existence of valid arguments. The latter involve the notions of argument structure and justification…

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally…

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under…

This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set…

We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…