Related papers: Russellian Propositional Logic and the BHK Interpr…
Representing and navigating hierarchy is a fundamental primitive of reasoning. Large language models have demonstrated proficiency in a wide variety of tasks requiring hierarchical reasoning, but there exists limited analysis on how the…
Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted,…
We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed…
Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical…
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented…
The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
Epistemic reasoning requires agents to infer the state of the world from partial observations and information about other agents' knowledge. Prior work evaluating LLMs on canonical epistemic puzzles interpreted their behavior through a…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
The logic of bunched implications (BI) can be seen as the free combination of intuitionistic propositional logic (IPL) and intuitionistic multiplicative linear logic (IMLL). We present here a base-extension semantics (B-eS) for BI in the…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…