Popular Semantics Research Articles

Complexity of abstract argumentation under a claim-centric view

Abstract argumentation frameworks have been introduced by Dung as part of an argumentation process, where arguments and conflicts are derived from a given knowledge base. It is solely this relation between arguments that is then used in order to identify acceptable sets of arguments. A final step concerns the acceptance status of particular statements by reviewing the actual contents of the acceptable arguments. Complexity analysis of abstract argumentation so far has neglected this final step and is concerned with argument names instead of their contents, i.e. their claims. As we outline in this paper, this is not only a slight deviation but can lead to different complexity results. We, therefore, give a comprehensive complexity analysis of abstract argumentation under a claim-centric view and analyse the four main decision problems under seven popular semantics. In addition, we also address the complexity of common sub-classes and introduce novel parameterisations – which exploit the nature of claims explicitly – along with fixed-parameter tractability results.

Complexity of Abstract Argumentation under a Claim-Centric View

Abstract argumentation frameworks have been introduced by Dung as part of an argumentation process, where arguments and conflicts are derived from a given knowledge base. It is solely this relation between arguments that is then used in order to identify acceptable sets of arguments. A final step concerns the acceptance status of particular statements by reviewing the actual contents of the acceptable arguments. Complexity analysis of abstract argumentation so far has neglected this final step and is concerned with argument names instead of their contents, i.e. their claims. As we outline in this paper, this is not only a slight deviation but can lead to different complexity results. We, therefore, give a comprehensive complexity analysis of abstract argumentation under a claim-centric view and analyse the four main decision problems under seven popular semantics. In addition, we also address the complexity of common sub-classes and introduce novel parameterisations – which exploit the nature of claims explicitly – along with fixed-parameter tractability results.

Lewis meets Brouwer: Constructive strict implication

C.I. Lewis invented modern modal logic as a theory of “strict implication” ⥽. Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than □ and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the “strength” axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction has been discovered by the functional programming community in their study of “arrows” as contrasted with “idioms”. Our particular focus is on arithmetical interpretations of intuitionistic ⥽ in terms of preservativity in extensions of HA, i.e., Heyting’s Arithmetic.

Managing Different Sources of Uncertainty in a BDI Framework in a Principled Way with Tractable Fragments

The Belief-Desire-Intention (BDI) architecture is a practical approach for modelling large-scale intelligent systems. In the BDI setting, a complex system is represented as a network of interacting agents - or components - each one modelled based on its beliefs, desires and intentions. However, current BDI implementations are not well-suited for modelling more realistic intelligent systems which operate in environments pervaded by different types of uncertainty. Furthermore, existing approaches for dealing with uncertainty typically do not offer syntactical or tractable ways of reasoning about uncertainty. This complicates their integration with BDI implementations, which heavily rely on fast and reactive decisions. In this paper, we advance the state-of-the-art w.r.t. handling different types of uncertainty in BDI agents. The contributions of this paper are, first, a new way of modelling the beliefs of an agent as a set of epistemic states. Each epistemic state can use a distinct underlying uncertainty theory and revision strategy, and commensurability between epistemic states is achieved through a stratification approach. Second, we present a novel syntactic approach to revising beliefs given unreliable input. We prove that this syntactic approach agrees with the semantic definition, and we identify expressive fragments that are particularly useful for resource-bounded agents. Third, we introduce full operational semantics that extend CAN, a popular semantics for BDI, to establish how reasoning about uncertainty can be tightly integrated into the BDI framework. Fourth, we provide comprehensive experimental results to highlight the usefulness and feasibility of our approach, and explain how the generic epistemic state can be instantiated into various representations.

On efficiently estimating the probability of extensions in abstract argumentation frameworks

Probabilistic abstract argumentation is an extension of Dung's abstract argumentation framework with probability theory. In this setting, we address the problem of computing the probability Pr sem ( S ) that a set S of arguments is an extension according to a semantics sem . We focus on four popular semantics (i.e., complete , grounded , preferred and ideal-set ) for which the state-of-the-art approach is that of estimating Pr sem ( S ) by using a Monte-Carlo simulation technique, as computing Pr sem ( S ) has been proved to be intractable. In this paper, we propose a new Monte-Carlo simulation approach which exploits some properties of the above-mentioned semantics for estimating Pr sem ( S ) using much fewer samples than the state-of-the-art approach, resulting in a significantly more efficient estimation technique. • A new Monte-Carlo-based technique for estimating the probability that a set of arguments is an extension is proposed. • The performances of the proposed technique are thoroughly analyzed both experimentally and theoretically. • The proposed technique outperforms the state of the art.

On the Complexity of Probabilistic Abstract Argumentation Frameworks

Probabilistic abstract argumentation combines Dung’s abstract argumentation framework with probability theory in order to model uncertainty in argumentation. In this setting, we address the fundamental problem of computing the probability that a set of arguments is an extension according to a given semantics. We focus on the most popular semantics (i.e., admissible , stable , complete , grounded , preferred , ideal-set , ideal , stage , and semistable ) and show the following dichotomy result: computing the probability that a set of arguments is an extension is either FP or FP # P -complete depending on the semantics adopted. Our polynomial-time results are particularly interesting, as they hold for some semantics for which no polynomial-time technique was known so far.

Naive Modus Ponens and Failure of Transitivity

In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and false consequent. I respond on behalf of the non-transitive approach. I argue that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the conditional in semantics for non-transitive entailment. I proceed to generalize the semantic idea of the conditional and show that the most popular semantics for non-transitive entailment satisfies the new formulation.

Automatic verification of temporal-epistemic properties of cryptographic protocols

We present a technique for automatically verifying cryptographic protocols specified in the mainstream specification language CAPSL. We define a translation from CAPSL models into interpreted systems, a popular semantics for temporal-epistemic logic, and rewrite CAPSL goals as temporal-epistemic specifications. We present a compiler that implements this translation. The compiler links to the symbolic model checker MCMAS. We evaluate the technique on protocols in the Clark-Jacobs library and in the SPORE repository against custom secrecy and authentication requirements.

On Bradley’s preservation condition for conditionals

Bradley has argued that a truth-conditional semantics for conditionals is incompatible with an allegedly very weak and intuitively compelling constraint on the interpretation of conditionals. I argue that the example Bradley offers to motivate this constraint can be explained along pragmatic lines that are compatible with the correctness of at least one popular truth-conditional semantics for conditionals.

Pfanzagl exchanges diagnose an anomaly in expected utility decision theory

Johann Pfanzagl proposed an additional decision axiom in 1959, complementary to the usual axioms, which would have tightly restricted permissible monetary utility functions. Subsequent debate partially clarified previously unacknowledged normative issues, and ended with orthodox consensus favoring a principled reform of practice. An analytical device contributed by Pfanzagl is extended here to show that the consensus practice sometimes conflicts with a principle often expressed as a continuity axiom, in situations as simple as Allais’ famous example. The axioms have from their beginnings been recognized as incomplete, so these new exceptions cannot much threaten the axioms’ role in such theories as a popular semantics for subjective probability. However, the paper suggests an enhancement of sensitivity analysis in applied work, sometimes overruling orthodox advice.

On the need for a popular formal semantics

The technology transfer from semantics research to mainstream computing has been hampered by specialization of techniques at the expense of calculational clarity. A "popular semantics" is proposed as a remedy.

On the need for a popular formal semantics

The technology transfer from research to mainstream computing has been hampered by specialization of techniques at the expense of calculational clarity. A popular semantics is proposed as a remedy.

The Narrow Semantics of Names

Narrow semantics is about the relation between utterance and thought: given a sentence, what beliefs (or desires) does it express; or, conversely, given your beliefs (and desires), what sentences is it linguistically proper for you to assent to? I would like to call this just 'semantics'. But unfortunately some philosophers have adopted a technical use of 'semantics' in which it refers to the relation between words and the world, rather than words and thought. The central epithet of semantics, in this technical sense, is 'true'. It is natural to think, however, that words latch onto the world only via people's thoughts. There is the relation between the words and the thought, which would be the same whatever the state of the world; and there is the relation between the thought and the world, which makes the thought true. Only the first of these relations would naturally be seen as specifically linguistic, within the scope of semantics. However, we need not quibble about terminology. The main point is that my topic is not the currently popular truth-conditional semantics. My topic is the narrow semantics of names and general terms. We can treat general terms as names-of sets, properties or whatever-by reading 'Fa' as 'a is a member of F', or 'a has F' or whatever.

The meaning of menopause in a newfoundland fishing village

A comparison of etic and emic options for climacteric research shows that the emic option is best suited to the study of the meaning of menopause in the Southwest coast Newfoundland outport fishing village of Grey Rock Harbour. Standard menopause survey instruments, as the Neugarten Attitudes Toward Menopause checklist (1963) and the Datan et al. Sociocultural Patterns and the Involutional Crisis interview schedule (1981) were administered to 38 women and found to be of limited utility because they assume the following: that respondents can rank stimuli along linearly constructed continuums, that the questionnaire items contain sufficient contextual information for Harbour women to make psychosocial judgements such as agree and disagree, and that respondents are capable of and experience no difficulty in making public pronouncements based on insightful self-evaluations. More qualitative ethnographic description and emic analysis address, yet go beyond, the popular semantics of menopause to explore the meaning of middle-aging in the symbolic, moral and institutional spheres of Harbour life. For more suitable context for understanding the role that sociocultural factors can play in shaping women's experience of middle-aging, in depth analyses of the following are offered: the continued importance of the fishery and the idealized social image of outport Newfoundlanders as a "tough race"; the expectation that women should endure hardship and solve problems rather than create them; and the strict enforcement of an egalitarian ethic throughout the community.