Related papers: On the Unity of Logic: a Sequential, Unpolarized A…
Unsupervised methods are widely used to induce latent semantic structure from large text collections, yet their outputs often contain incoherent, redundant, or poorly grounded clusters that are difficult to validate without labeled data. We…
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…
An increasing amount of research in Natural Language Inference (NLI) focuses on the application and evaluation of Large Language Models (LLMs) and their reasoning capabilities. Despite their success, however, LLMs are still prone to factual…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming…
In this paper, we generalize modal $\mu$-calculus to the non-distributive (lattice-based) modal $\mu$-calculus and formalize some scenarios regarding categorization using it. We also provide a game semantics for the developed logic. The…
In recent years, Large Language Models (LLMs) have demonstrated remarkable generative abilities, but can they judge the quality of their own generations? A popular concept, referred to as self-refinement, postulates that LLMs can detect and…
Following a characterization [10] of locally tabular logics with finitary (or unitary) unification by their Kripke models we determine the unification types of some intermediate logics (extensions of {\sf INT}). There are exactly four…
A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
This article presents a new game semantics for Martin-L\"of type theory (MLTT), in which each game is equipped with selected isomorphism strategies that represent (computational) proofs for (intensional) equality between strategies on the…
Concurrent stochastic games are an important formalism for the rational verification of probabilistic multi-agent systems, which involves verifying whether a temporal logic property is satisfied in some or all game-theoretic equilibria of…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas…
Abstract. Matching logic cannot handle concurrency. We introduce concurrent matching logic (CML) to reason about fault-free partial correctness of shared-memory concurrent programs. We also present a soundness proof for concurrent matching…
We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general term-orderings (instead of level mappings), like it is done in transformational approaches to logic program…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
In-Context Learning (ICL) allows Large Language Models (LLMs) to adapt to new tasks with just a few examples, but their predictions often suffer from systematic biases, leading to unstable performance in classification. While calibration…
Game logic was introduced by Rohit Parikh in the 1980s as a generalisation of propositional dynamic logic (PDL) for reasoning about outcomes that players can force in determined 2-player games. Semantically, the generalisation from programs…
In this paper, we introduce game-theoretic semantics (GTS) for Qualitative Choice Logic (QCL), which, in order to express preferences, extends classical propositional logic with an additional connective called ordered disjunction. Firstly,…