Related papers: Bilateral base-extension semantics
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with…
In this paper, we propose a fresh perspective on argumentation semantics, to view them as a relational database. It offers encapsulation of the underlying argumentation graph, and allows us to understand argumentation semantics under a…
We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
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…
Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the…
It is demonstrated that under the hypothesis of boundedness, the semantics appears as a property of spontaneous physical processes. It turns that both semantic structure and semantic meaning have their own physical agents each of which is…
Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming…
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on 'proof' (as opposed to 'truth'). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a…
This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. It builds on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of…
The standard notion of formal theory, in Logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
This paper studies a fundamental mechanism of how to detect a conflict between arguments given sentiments regarding acceptability of the arguments. We introduce a concept of the inverse problem of the abstract argumentation to tackle the…