Related papers: Normative Conditional Reasoning as a Fragment of H…
For half a century, authors have weakened the rule of necessitation in various more or less ad hoc ways in order to make inconsistent systems consistent. More recently, necessitation was weakened in a systematic way, not for the purpose of…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
Building on work by Alfonseca et al. (2021), we study the conditions necessary for it to be logically possible to prove that an arbitrary artificially intelligent machine will exhibit certain behavior. To do this, we develop a formalism…
Realizability interprets propositions as specifications for computational entities in programming languages. Specifically, syntactic realizability is a powerful machinery that handles realizability as a syntactic translation of propositions…
We consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be elegantly and directly expressed using default negation (negation-as-failure) and strong negation present in answer set programming…
The paper proposes a fresh look at the concept of goal and advances that motivational attitudes like desire, goal and intention are just facets of the broader notion of (acceptable) outcome. We propose to encode the preferences of an agent…
We define a novel neuro-symbolic framework, argumentative reward learning, which combines preference-based argumentation with existing approaches to reinforcement learning from human feedback. Our method improves prior work by generalising…
The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…
We introduce a monotone modal analogue of the intuitionistic (normal) modal logic IK using a translation into a suitable (intuitionistic) first-order logic. We axiomatise the logic and give a semantics by means of intuitionistic…
Classical Decision Theory provides a normative framework for representing and reasoning about complex preferences. Straightforward application of this theory to automate decision making is difficult due to high elicitation cost. In response…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…