Related papers: A logic for default deontic reasoning
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
Large language models have shown unprecedented abilities in generating linguistically coherent and syntactically correct natural language output. However, they often return incorrect and inconsistent answers to input questions. Due to the…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification…
Diagnostic reasoning has been characterized logically as consistency-based reasoning or abductive reasoning. Previous analyses in the literature have shown, on the one hand, that choosing the (in general more restrictive) abductive…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts,…
The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…
G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic…
Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…
We consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under answer set semantics. New information is incorporated into the current knowledge base subject to a causal rejection principle…
In ASPIC-style structured argumentation an argument can rebut another argument by attacking its conclusion. Two ways of formalizing rebuttal have been proposed: In restricted rebuttal, the attacked conclusion must have been arrived at with…
The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
A default theory can be characterized by its sets of plausible conclusions, called its extensions. But, due to the theoretical complexity of Default Logic (Sigma_2p-complete), the problem of finding such an extension is very difficult if…
Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent.…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…