Representation considerations for logical argumentation frameworks: Minimality, consistency, compactness, and logical preservation

This paper presents a logical framework derived from the Edinburgh Logical Framework (LF) that can be used to obtain compact representations of proofs and efficient proof checkers. These are essential ingredients of any application that manipulates proofs as first-class objects, such as a Proof-Carrying Code system, in which proofs are used to support easy validation of properties of safety-critical or untrusted code. Our framework, which we call LF/sub i/, inherits from LF the capability to encode various logics in a natural way. In addition, the LF/sub i/ framework allows proof representations without the high degree of redundancy that is characteristic of LF representations. The missing parts of LF/sub i/ proof representations can be reconstructed during proof checking by an efficient reconstruction algorithm. We also describe an algorithm that can be used to strip the unnecessary parts of an LF representation of a proof. The experimental data that we gathered in the context of a Proof-Carrying Code system shows that the savings obtained from using LF/sub i/ instead of LF can make the difference between practically useless proofs of several megabytes and manageable proofs of tens of kilobytes.

Logical relations are a central concept used to study various higher-order type theories and occur frequently in the proofs of a wide variety of meta-theorems. Besides extending the logical relation principle to more general languages, an important research question has been how to represent and thus verify logical relation arguments in logical frameworks. We formulate a theory of logical relations for Dependent Type Theory (DTT) with β η-equality which guarantees that any valid logical relation satisfies the Basic Lemma. Our definition is syntactic and reflective in the sense that a relation at a type is represented as a DTT type family but also permits expressing certain semantic definitions. We use the Edinburgh Logical Framework (LF) incarnation of DTT and implement our notion of logical relations in the type-checker Twelf. This enables us to formalize and mechanically decide the validity of logical relation arguments. Furthermore, our implementation includes a module system so that logical relations can be built modularly. We validate our approach by formalizing and verifying several syntactic and semantic meta-theorems in Twelf. Moreover, we show how object languages encoded in DTT can inherit a notion of logical relation from the logical framework.

Logic-based argumentation is a formal method for constructing, evaluating and comparing arguments. In this paper we address two (related) key issues concerning the representation of logical argumentation frameworks: how to describe them in a compact way, and how to move from one framework to another while preserving their basic logical characteristics. The results are applied to various forms of attack rules and different kinds of argumentative semantics, and are demonstrated for transitions between several 3-valued logics and classical logic. As a byproduct, our results are also used for converting logic-based argumentation frameworks to assumption-based argumentation frameworks.

In this paper we are interested in argument based reasoning for access control, for example in the context of agents negotiating access to resources or web services in virtual organizations. We use a logical framework which contains agents with objectives concerning access to a resource or provision of a service, including security objectives. The access control mechanism is described by a set of policy rules, that specify that access to a resource or service requires a specific set of credentials. Our contribution is a formalization of the reasoning about access control using a planning theory formalized in Dung’s abstract argumentation framework. We build on Amgoud’s argumentation framework for plan arguments, which is based on an adaptation of Dung’s notion of defence. Our formal argumentation framework allows arguments about the backward derivation of plans from objectives and policy rules (abduction), as well as arguments about the forward derivation of goals from general objectives. We show that reasoning about the feasibility of goals requires mixed goal-plan arguments, and we show how to formalize the plan arguments in Dung’s framework without adapting the notion of defence.KeywordsAccess ControlLogic ProgrammingIntegrity ConstraintPolicy RuleArgumentation TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Logical argumentation is a well-known approach to modeling non-monotonic reasoning with conflicting information. In this paper we provide a comprehensive postulate-based study of properties of logical argumentation frameworks and a full characterization of their semantics and inference relations. In this way we identify well-behaved formal argumentative models of drawing logically justified inferences from a given set of possibly conflicting defeasible, as well as strict assumptions. Given some desiderata in terms of rationality postulates, we consider the conditions that an argumentation framework should fulfill for the desiderata to hold. One purpose of this approach is to assist designers to “plug-in” pre-defined formalisms according to actual needs. To this end, we present a classification of argumentation frameworks relative to the types of attacks they implement. In turn, for each class we determine which desiderata are satisfied. Our study is highly abstract, supposing only a minimal set of requirements on the considered underlying deductive systems, and in this way covering a broad range of formalisms, including classical, intuitionistic and modal logics.

We present a novel computational approach to resolving conflicts among norms by nonmonotonic normative reasoning (in constrained I/O logics). Our approach extends standard sequent-based proof systems and makes them more adequate to nonmonotonic reasoning by adding to the sequents annotations that keep track of what is known about the defeasible status of the derived sequents. This makes transparent the reasons according to which norms should be applicable or inapplicable, and accordingly the sequents that make use of such norms are accepted or retracted. We also show that this proof theoretic method has tight links to the semantics of formal argumentation frameworks. The outcome of this paper is thus a threefold characterization result that relates, in the context of nonmonotonic normative reasoning, three traditional ingredients of AI-based reasoning methods: maximally consistent sets of premises (in constrained I/O logics), derived sequents (which are accepted in corresponding annotated sequent calculi), and logical arguments (that belong to the grounded extensions of the induced logical argumentation frameworks).

Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a con- fluence point for many alternative logical frameworks. Dierent formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (de- feasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other conflicting arguments. In this context, defeasi- ble consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators Carg and Cwar intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDSar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference op- erators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. Mathematics Subject Classification (2000). Primary 03B22; Secondary 03B42.

Compared to abstract argumentation theory which encapsulates the exact nature of arguments, logic-based argumentation is more specific and represents arguments in formal logic. One significant advantage of logic-based argumentation over abstract argumentation is that it can directly benefit from logical properties such as logical consistency, promoting adherence of an argumentation framework to rational principles. On the other hand, a logical argumentation framework based on classical logic has been also reported of its less-than-desirable utility. In this work we show a way of enhancing utility without sacrificing so much of rationality. We propose a rational argumentation framework with just classical logic sentences and a belief contraction operation. Despite its minimalistic appearance, this framework can characterise attack strengths, allowing us to facilitate coalition profitability and formability semantics we previously defined for abstract argumentation.

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are induced by the extended (hypersequent-based) frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics (like the intermediate logic LC, the modal logic S5, and the relevance logic RM), which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties.

In this paper, we study the impact of two notions of core on the output of ranking semantics in logical argumentation frameworks. We consider the existential rules fragment, a language widely used in Semantic Web and Ontology Based Data Access applications. Using burden semantics as example we show how some ranking semantics yield different outputs on the argumentation graph and its cores. We extend existing results in the literature regarding core equivalences on logical argumentation frameworks and propose the first formal characterisation of core-induced modification for a class of ranking semantics satisfying given postulates.

In this paper, we study the impact of two notions of core on the output of ranking semantics in logical argumentation frameworks. We consider the existential rules fragment, a language widely used in Semantic Web and Ontology Based Data Access applications. Using burden semantics as example we show how some ranking semantics yield different outputs on the argumentation graph and its cores. We extend existing results in the literature regarding core equivalences on logical argumentation frameworks and propose the first formal characterisation of core-induced modification for a class of ranking semantics satisfying given postulates.

In 1995, in his seminal paper introducing the abstract argumentation framework, Dung has also established the first relationship between this framework and a logical framework (in this case: logic programming). Since that time, a lot of work have pursued this path, proposing different definitions, uses and exhibiting distinct relationships between argumentation and logic. In this paper, we present a survey of existing works about this topic and more especially those that address the following question: “How logic has been used for capturing various aspects or parts of Dung’s argumentation”. This survey covers many different approaches but is not intended to be totally exhaustive due to the huge quantity of papers in this scope. Moreover, due to the fact that each approach has its own specificities, sometimes antagonistic with the other approaches, and is also justified by its own context of definition or use, the aim of this survey is not to identify one approach as being better than another.

Food advertising and self‐regulation: A view from the trenches

As a research methodology, logical argumentation draws from seemingly disconnected factors and weaves them into a single explanatory matrix. This chapter draws from early Greek terms for the word "ethos" and overlays them with the poststructuralist Henri Lefebvre's theory of space as a social production. The result is a logical framework that offers a new generalizable construct: ethos-intensive objects (EIOs). EIOs, in their ability to bridge between material forms and human feelings of attachment to locale, are a new way to assess the ethos of any locality. Interiority here places the researcher into the communal outlook of any given locale, in ways that perhaps are not otherwise comprehensible with respect to sense of place.

This is a survey of some recent results relating Dung-style semantics for different types of logical argumentation frameworks and several forms of reasoning with maximally consistent sets (MCS) of premises. The related formalsims are also examined with respect to some rationality postulates and are carried on to corresponding proof systems for non-monotonic reasoning.