A puzzle about narrative progression and causal reasoning

This chapter argues that key to an analysis of narrative progression are aspectual constraints imposed by coherence relations. This argument is based on a discourse like “A cat bit into a mouse while it was wiggling its tail. It was dead”. The fact that it’s infelicitous is remarkable given that the following is fine: “A mouse was dead. A cat bit into it while it was wiggling its tail”. The chapter explains these data in two steps. First, it proposes definitions for the coherence relations, RESULT and EXPLANATION, in which the former, but not the latter, rules out stative arguments. Second, it provides axioms in a default logic which predict the conditions under which these and competing coherence relations are typically inferred. It provides independent evidence for the proposed analysis from discourses involving exclamatives, temporal indexicals, and deverbals. It also considers discourses that challenge the analysis involving perspectival expressions.

Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming

Approximation fixpoint theory (AFT) constitutes an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

Ways of transforming the metaphysical thinkingin the “conceptless language” of the late M. Heidegger

The article provides an analysis of the concept of “conceptless language” in the works of the late Martin Heidegger. The formation of a “conceptless language” is one of the most mysterious phenomena in the philosophy of the thinker. The specific structure of this lan­guage is one of the main criticisms of the later works of the philosopher and the opposition of Heidegger as the author of “Sein und Zeit” to Heidegger of the period “Beiträge zur Philosophie. Vom Ereignis”. The article explains the specific structure of the “concept-free language”, the reasons for its creation and its role in the late Heidegger philosophy. An at­tempt is made to reveal the hidden logic of a “conceptless language” and the principles by which it is guided. The search for the logic of a “conceptless language” is carried out through consideration of some of its aspects: a way of expressing thoughts, features of the style of argumentation, and a method of forming terms. An analysis of these aspects shows how Heidegger seeks to overcome the problem of the so-called “refusal” (Versagen) of the language that arose after writing “Sein und Zeit”. In search of a language correspond­ing to the transition to a different beginning, the principles of the late Heidegger hermeneutic methodology are formed: the “principle of intentional incomprehensibility” of terms, “default logic”, clarification of terms through their “internal form”, method of “thoughtful use of language” (besinnliche Sprachgebrauch). The analysis leads to the con­clusion that the profound change in thinking, which the late Heidegger sought on the way to another beginning, is impossible without the transformation of the language. Due to the fact that the existing “metaphysical” thinking is directly related to the conceptual lan­guage, a “non-conceptual language” opens the way for alternative thinking.

A logic of defeasible argumentation: Constructing arguments in justification logic

In the 1980s, Pollock’s work on default reasons started the quest in the AI community for a formal system of defeasible argumentation. The main goal of this paper is to provide a logic of structured defeasible arguments using the language of justification logic. In this logic, we introduce defeasible justification assertions of the type t : F that read as “t is a defeasible reason that justifies F”. Such formulas are then interpreted as arguments and their acceptance semantics is given in analogy to Dung’s abstract argumentation framework semantics. We show that a large subclass of Dung’s frameworks that we call “warranted” frameworks is a special case of our logic in the sense that (1) Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and (2) Dung’s warranted frameworks always have multiple justification logic instantiations called “realizations”. We first define a new justification logic that relies on operational semantics for default logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. This enables us to formalize non-monotonic justifications that prompt extension revision already for normal default theories. Then we present our logic as a system for abstract argumentation with structured arguments. The format of conflicting reasons overlaps with the idea of attacks between arguments to the extent that it is possible to define all the standard notions of argumentation framework extensions. Using the definitions of extensions, we establish formal correspondence between Dung’s original argumentation semantics and our operational semantics for default theories. One of the results shows that the notorious attack cycles from abstract argumentation cannot always be realized as justification logic default theories.

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

Reasoning About Prescription and Description Using Prioritized Default Rules

In this paper we introduce a prioritized default logic. We build this logic modularly from Standard Deontic Logic by the addition of default rules and priorities among them. Our main aim is to provide a logical framework to reason about scenarios where prescriptive and descriptive statements coexist and may be incomplete and contradictory. We motivate and illustrate the technical elements of our work with the use of examples (classical, and coming from software engineering). In addition, we present sound, complete, and terminating (with loop check) tableau-based proof calculi for credulous and sceptical reasoning in our logic.