Epistemic Extension Research Articles

A unified logical framework for explanations in classifier systems

AbstractRecent years have witnessed a renewed interest in the explanation of classifier systems in the field of explainable AI (XAI). The standard approach is based on propositional logic. We present a modal language which supports reasoning about binary input classifiers and their properties. We study a family of classifier models, axiomatize it as two proof systems regarding the cardinality of the language and show completeness of our axiomatics. Moreover, we show that the satisfiability checking problem for our modal language is NEXPTIME-complete in the infinite-variable case, while it becomes polynomial in the finite-variable case. We moreover identify an interesting NP fragment of our language in the infinite-variable case. We leverage the language to formalize counterfactual conditional as well as a variety of notions of explanation including abductive, contrastive and counterfactual explanations and biases. Finally, we present two extensions of our language: a dynamic extension by the notion of assignment enabling classifier change and an epistemic extension in which the classifier’s uncertainty about the actual input can be represented.

Game equivalence and expressive power of game description languages: a bisimulation approach

Abstract Bisimulations are a key notion to study the expressive power of a modal language. This paper studies the expressivity of Game Description Language (GDL) and its epistemic extension Epistemic GDL (EGDL) through a bisimulation approach. We first define a notion of bisimulation for GDL and prove that it coincides with the indistinguishability of GDL formulas. Based on it, we establish a characterization of the definability of GDL in terms of $k$-bisimulations. Then we design novel notions of bisimulation for EGDL and obtain characterizations of the expressive power of EGDL in terms of them. These characterizations provide a powerful tool to identify the expressive power of game description languages. Finally, we demonstrate with real games that bisimulation can be generalized to capture a wide range of game equivalence.

DOING WITHOUT ACTION TYPES

AbstractThis paper explores the analysis of ability, where ability is to be understood in the epistemic sense—in contrast to what might be called a causal sense. There are plenty of cases where an agent is able to perform an action that guarantees a given result even though she does not know which of her actions guarantees that result. Such an agent possesses the causal ability but lacks the epistemic ability. The standard analysis of such epistemic abilities relies on the notion of action types—as opposed to action tokens—and then posits that an agent has the epistemic ability to do something if and only if there is an action type available to her that she knows guarantees it. We show that these action types are not needed: we present a formalism without action types that can simulate analyzes of epistemic ability that rely on action types. Our formalism is a standard epistemic extension of the theory of “seeing to it that”, which arose from a modal tradition in the logic of action.

Autoepistemic equilibrium logic and epistemic specifications

Epistemic specifications extend disjunctive answer-set programs by an epistemic modal operator that may occur in the body of rules. Their semantics is in terms of world views, which are sets of answer sets, and the idea is that the epistemic modal operator quantifies over these answer sets. Several such semantics were proposed in the literature. We here propose a new semantics that is based on the logic of here-and-there: we add epistemic modal operators to its language and define epistemic here-and-there models. We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from epistemic here-and-there models in exactly the same way as Pearce's equilibrium models are obtained from here-and-there models, viz. by minimising truth; they provide an epistemic extension of equilibrium logic. The latter are obtained from the former by maximising the set of epistemic possibilities, and they provide a new semantics for Gelfond's epistemic specifications. For both semantics we establish a strong equivalence result: we characterise strong equivalence of two epistemic programs by means of logical equivalence in epistemic here-and-there logic. We finally compare our approach to the existing semantics of epistemic specifications and discuss which formalisms provide more intuitive results by pointing out some formal properties a semantics proposal should satisfy.

Epistemic autonomy and group knowledge

I connect two increasingly popular ideas in social epistemology—group knowledge and epistemic extension—both departures from mainstream epistemological tradition. In doing so, I generate a framework for conceptualizing and organizing contemporary epistemology along several core axes. This, in turn, allows me to delineate a largely unexplored frontier in group epistemology. The bulk of extant work in group epistemology can be dubbed intra-group epistemology: the study of epistemically salient happenings within groups. I delineate and attempt to motivate what I dub inter-group epistemology: the study of epistemically salient happenings between groups and other subjects and entities.

Model-checking graded computation-tree logic with finite path semantics

This paper introduces Graded Computation Tree Logic with finite path semantics (GCTLf⁎, for short), a variant of Computation Tree Logic CTL⁎, in which path quantifiers are interpreted over finite paths and can count the number of such paths. State formulas of GCTLf⁎ are interpreted over Kripke structures. The syntax of GCTLf⁎ has path quantifiers of the form E≥gψ which express that there are at least g many distinct finite paths that satisfy ψ. After defining and justifying the logic GCTLf⁎, we solve its model checking problem and establish that its computational complexity is PSPACE-complete. Moreover, we investigate GCTLf⁎ under the imperfect information setting. Precisely, we introduce GCTLKf⁎, an epistemic extension of GCTLf⁎ and prove that the model checking problem also in this case is PSPACE-complete.

GROUPS CAN KNOW HOW

Abstract One can know how to ride a bicycle, play the cello, or collect experimental data. But who can know how to properly ride a tandem bicycle, perform a symphony, or run a high-energy physics experiment? Reductionist analyses fail to account for these cases strictly in terms of the individual know-how involved. Nevertheless, it doesn’t follow from non-reductionism that groups possess this know-how. One must first show that epistemic extension cannot obtain. This is the idea that individuals can possess knowledge even when others possess some of the epistemic materials (e.g. evidence possessed, abilities exercised) generating it. I show that only knowledge-that can be epistemically extended, not knowledge-how. Appeal to epistemic extension is a viable way of avoiding group knowledge-that ascriptions but not group knowledge-how ascriptions. Therefore, groups can know how.

An Epistemic Approach to Nondeterminism: Believing in the Simplest Course of Events

This paper describes an approach for reasoning in a dynamic domain with nondeterministic actions in which an agent’s (categorical) beliefs correspond to the simplest, or most plausible, course of events consistent with the agent’s observations and beliefs. The account is based on an epistemic extension of the situation calculus, a first-order theory of reasoning about action that accommodates sensing actions. In particular, the account is based on a qualitative theory of nondeterminism. Our position is that for commonsense reasoning, the world is most usefully regarded as deterministic, and that nondeterminism is an epistemic phenomenon, arising from an agent’s limited awareness and perception. The account offers several advantages: an agent has a set of categorical (as opposed to probabilistic) beliefs, yet can deal with equally-likely outcomes (such as in flipping a fair coin) or with outcomes of differing plausibility (such as an action that on rare occasions may fail). The agent maintains as its set of contingent beliefs the most plausible, or simplest, picture of the world, consistent with its beliefs and actions it believes it executed; yet it may modify these in light of later information.

Res extensaetres cogitansdemaqasid as-shari’ah

Purpose– This paper aims to undertake a critical evaluation of the purpose and objective of Islamic Law, namely,maqasid as-shari’ah, as it has evolved in Islamic scholastic experience. But, the greater philosophy and potential ofmaqasid as-shari’ahwithin the great design of the monotheistic law,sunnat-Allah, is explained. Such explanation is carried out in the light of the core of Islamic epistemology that directly induces Islamic Law.Design/methodology/approach– This critical evaluation is pursued in the light of the epistemological worldview and its methodical formalism of unity of knowledge contra a differentiated and conflicting view of human experience in rationalism. The episteme of unity of knowledge isTawhidas the law of everything in the precept of unity as understood by the monotheistic law,sunnat-Allah. In the light of the extendibility ofmaqasid as-shari’ahacross the relationally unifying domain ofsunnat-Allah, the potentiality ofshari’ahin terms ofres extensa(epistemic extension) andres cogitans(cognitive capacity) is discussed.Findings– Various occidental thoughts in this quest for extendibility of the epistemic totality are critically examined by theTawhidimonotheistic law. The universality of theTawhidilaw of monotheism in respect of its characteristics ofres extensaandres cogitansis studied to bring out the potentiality ofmaqasid as-shari’ah. Thereby, the new vision of inter-systemic extensions across diverse domains of intellection interactively unified together is formalized. This formalism goes beyond the existing limits ofmaqasid as-shari’ahconfined as it is to worldly socioeconomic affairs (muamalat).Research limitations/implications– A much broader investigation is opened up by this paper that can be extended by academic work.Practical implications– The practical support of the criticism against both the idea ofshari’ah-compliance and the incomplete implication ofmaqasid as-shari’ahas presently understood among Islamic scholars is carried out by a detailed empirical work. The extension to the choice of a new financial instrument of Foreign Trade Financing Certificate is introduced.Social implications– The critical discussion launched in reference to the wider meaning, objective and purpose ofmaqasid as-shari’ahunder the epistemology of theTawhidimethodological worldview results in the substantive understanding ofmaslaha, well-being.Maslahaas well-being forms the ultimate index of socio-scientific valuation undermaqasid as-shari’ahin the light of theTawhidiepistemological worldview. Thereby, the perspective of socioeconomic development, and more extensively socio-scientific intellection, is brought out as extensively participatory evolutionary process under the principle of unity of knowledge (Tawhidiepisteme). Brief examples are invoked to establish this fact. An example of measured multidimensional well-being (maslaha) as the final index of participatory organic relations thatmaqasid as-shari’ahought to project in reference toTawhidimethodological worldview is represented.Originality/value– This is a distinctively original paper in an area that has not been investigated thus far. Besides, much scope for further intellectual investigation is opened up.

Constrained Epistemic Extension on Agent Knowledge Acquisition

In multi-agent systems, a number of autonomous pieces of software (the agents) interact in order to execute complex tasks. This paper proposes a logic framework portrays agent’s communication protocols in the multi-agent systems and a dynamic negotiation model based on epistemic default logic was introduced in this framework. In this paper, we use the constrained default rules to investigate the extension of dynamic epistemic logic, and constrained epistemic extension construct an efficient negotiation strategy via constrained epistemic default reasoning, which guarantees the important natures of extension existence and semi-monotonicity. We also specify characteristic of the dynamic updating when agent learn new knowledge in the logical framework. The method for the information sharing signify the usefulness of logical tools carried out in the dynamic process of information acquisition, and the distributed intelligent information processing show the effectiveness of reasoning default logic in the dynamic epistemic logic theory.

What groups do, can do, and know they can do: an analysis in normal modal logics

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that has been proposed in previous work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL.

Model checking cooperation, knowledge, and time—a case study

Alternating-time Temporal Logic (ATL) is a logic developed by Alur, Henzinger, and Kupferman for reasoning about coalitional powers in multiagent systems. Since what agents can achieve in a specific state will in general depend on the knowledge they have in that state, in an earlier paper we proposed Alternating-time Temporal Epistemic Logic (ATEL), an epistemic extension to ATL which is interpreted over Alternating-time Temporal Epistemic Transition Systems. The logic ATEL shares with its ancestor ATL the property that its model checking problem is tractable. However, while model checkers have been implemented for ATL, no model checker yet exists for ATEL, or indeed for epistemic logics in general. The aim of this paper is to demonstrate, using the alternating bit protocol as a detailed case study, how existing model checkers for ATL can be deployed to verify epistemic properties.

A theory and implementation of cognitive mobile robots

We describe an approach to reasoning agents which is based on a formal theory of actions and is actually implemented on a mobile robot working in an oce environment. From an epistemological viewpoint, our proposal is originated by the correspondence between Dynamic Logics and Description Logics. Specically, we consider an epistemic extension of Description Logics to provide a new theoretical framework for the representation of dynamic systems, where the agent’s reasoning is based on its knowledge about the world. In this setting, we obtain a weaker notion of logical inference, thus simplifying the reasoning task. From a practical viewpoint, we use a general purpose knowledge representation system based on Description Logics and its associated reasoning tools, in order to plan the actions of the mobile robot ‘Tino’, starting from the knowledge about the environment and the action specication. In addition, we exploit the robot’s capabilities in order to integrate the execution of the plan with reactive behaviours, thus enabling the agent to accomplish its tasks in the real world.