Transreal Numbers and Sentient Logic

This chapter introduces the basic concepts of Total Semantics based on transreal numbers, a new field of mathematics in which division of zero is allowed. In the logic created from the transreals, it is possible to evaluate non-propositional objects such as sensations or feelings as having truth value. By covering all semantical possibility, transreal semantics enables a “poetical discourse” based on images and an immediate intuition of reality, an intuition that is both sensory and mental. This describes, and defines, a new type of epistemic operation—a sentient one—and leads to the possibility of developing a formal epistemic logic that assesses how we obtain or acquire knowledge from the perspective of sentient agents.

Relating Semantics for Epistemic Logic

The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can be associated with intuitive systems of relating logic. As a final step, I will focus on the logic of knowledge based on justification logic and show how relating semantics helps us to provide an elegant solution to some problems related to the standard interpretation of the explicit epistemic operators.

A Semantics for Hyperintensional Belief Revision Based on Information Bases

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.

Determining Action Reversibility in STRIPS Using Answer Set and Epistemic Logic Programming

In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem of action reversibility for the STRIPS fragment of PDDL. For these, we use ASP, as well as Epistemic Logic Programming (ELP), an extension of ASP with epistemic operators, and compare and contrast their strengths and weaknesses.

On the Epistemic Logic of Incomplete Argumentation Frameworks

We study the relation between two existing formalisms: incomplete argumentation frameworks (IAFs) and epistemic logic of visibility (ELV). We show that the set of completions of a given IAF naturally corresponds to a specific equivalence class of possible worlds within the model of visibility. This connection is further strengthened in two directions. First, we show how to reduce argument acceptance problems of IAFs to ELV model-checking problems. Second, we highlight the epistemic assumptions that underlie IAFs by providing a minimal epistemic logic for IAFs.

Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

Extending the popular answer set programming paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, that is, contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently.

DEL-based Epistemic Planning for Human-Robot Collaboration: Theory and Implementation

Epistemic planning based on Dynamic Epistemic Logic (DEL) allows agents to reason and plan from the perspective of other agents. The framework of DEL-based epistemic planning thereby has the potential to represent significant aspects of Theory of Mind in autonomous robots, and to provide a foundation for human-robot collaboration in which coordination is achieved implicitly through perspective shifts. In this paper, we build on previous work in epistemic planning with implicit coordination. We introduce a new notion of indistinguishability between epistemic states based on bisimulation, and provide a novel partition refinement algorithm for computing unique representatives of sets of indistinguishable states. We provide an algorithm for computing implicitly coordinated plans using these new constructs, embed it in a perceive-plan-act agent loop, and implement it on a robot. The planning algorithm is benchmarked against an existing epistemic planning algorithm, and the robotic implementation is demonstrated on human-robot collaboration scenarios requiring implicit coordination.