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Dialogue games are two-player logic games between a Proponent who puts forward a logical formula A as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which…
As Large Language Models (LLMs) are increasingly applied in high-stakes domains, their ability to reason strategically under uncertainty becomes critical. Poker provides a rigorous testbed, requiring not only strong actions but also…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
Large Language Models (LLMs) excel in generating personalized content and facilitating interactive dialogues, showcasing their remarkable aptitude for a myriad of applications. However, their capabilities in reasoning and providing…
Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be together formalized and studied logically. We consider several logics in the setting of causal multiteam…
We introduce a framework for reasoning about the security of computer systems using modal logic. This framework is sufficiently expressive to capture a variety of known security properties, while also being intuitive and independent of…
We study linear constraint system (LCS) games over the ring of arithmetic modulo $d$. We give a new proof that certain LCS games (the Mermin--Peres Magic Square and Magic Pentagram over binary alphabets, together with parallel repetitions…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Implicit content plays a crucial role in political discourse, where speakers systematically employ pragmatic strategies such as implicatures and presuppositions to influence their audiences. Large Language Models (LLMs) have demonstrated…
Large Language Models (LLMs) are able to improve their responses when instructed to do so, a capability known as self-correction. When instructions provide only a general and abstract goal without specific details about potential issues in…
We characterize common assumption of rationality of 2-person games within an incomplete information framework. We use the lexicographic model with incomplete information and show that a belief hierarchy expresses common assumption of…
Quite some work in the ATL-tradition uses the differences between various types of strategies (positional, uniform, perfect recall) to give alternative semantics to the same logical language. This paper contributes to another perspective on…
Game semantics is a trace-like denotational semantics for programming languages where the notion of legal observable behaviour of a term is defined combinatorially, by means of rules of a game between the term (the "Proponent") and its…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
Adding interaction to logic programming is an essential task. Expressive logics such as linear logic provide a theoretical basis for such a mechanism. Unfortunately, none of the existing linear logic languages can model interactions with…
Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes…
We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the…
Human languages have evolved to be structured through repeated language learning and use. These processes introduce biases that operate during language acquisition and shape linguistic systems toward communicative efficiency. In this paper,…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
Large Language Models (LLMs) are notorious for blending fact with fiction and generating non-factual content, known as hallucinations. To address this challenge, we propose an interactive system that helps users gain insight into the…