Related papers: Teaching Intuitionistic and Classical Propositiona…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…
Efficiently navigating complex environments requires agents to internalize the underlying logic of their world, yet standard world modelling methods often struggle with sample inefficiency, lack of transparency, and poor scalability. We…
This paper tries to justify the relevance of an introductory course in Mathematical Logic in the Philosophy curriculum for analyzing philosophical arguments in natural language. It is argued that the representation of the structure of…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
We introduce the logical grammar emdebbing (LGE), a model inspired by pregroup grammars and categorial grammars to enable unsupervised inference of lexical categories and syntactic rules from a corpus of text. LGE produces comprehensible…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
In this paper, we study logics of dependence on the propositional level. We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well…
In this Masters thesis we present an implementation of a fragment of "book HoTT" as an object logic for the interactive proof assistant Isabelle. We also give a mathematical description of the underlying theory of the Isabelle/Pure logical…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment…
We present the Natural Deduction Assistant (NaDeA) and discuss its advantages and disadvantages as a tool for teaching logic. NaDeA is available online and is based on a formalization of natural deduction in the Isabelle proof assistant. We…
On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic…
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…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Systems of deontic logic suffer either from being too expressive and therefore hard to mechanize, or from being too simple to capture relevant aspects of normative reasoning. In this article we look for a suitable way in between: the…
This paper makes a first step towards a logic of learning from experiments. For this, we investigate formal frameworks for modeling the interaction of causal and (qualitative) epistemic reasoning. Crucial for our approach is the idea that…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…