Related papers: Fixpoint 3-valued semantics for autoepistemic logi…
In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition…
Building on the analysis of Bonanno (Artificial Intelligence, 2025) we introduce a simple modal logic containing three modal operators: a unimodal belief operator, a bimodal conditional operator and the unimodal global operator. For each…
The continuous modal mu-calculus is a fragment of the modal mu-calculus, where the application of fixpoint operators is restricted to formulas whose functional interpretation is Scott-continuous, rather than merely monotone. By…
This paper extends the self-referential framework of Alpay Algebra into a multi-layered semantic game architecture where transfinite fixed-point convergence encompasses hierarchical sub-games at each iteration level. Building upon Alpay…
We study the decidability and expressiveness issues of $\mu$-calculus on data words and data $\omega$-words. It is shown that the full logic as well as the fragment which uses only the least fixpoints are undecidable, while the fragment…
Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of…
We apply to the semantics of Arithmetic the idea of ``finite approximation'' used to provide computational interpretations of Herbrand's Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for $\vee,…
The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with…
The logic underlying the Abella proof assistant includes mechanisms for interpreting atomic predicates through fixed point definitions that can additionally be treated inductively or co-inductively. However, the original formulation of the…
Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis…
Dynamic Epistemic Logic (DEL) is a family of multimodal logics that has proved to be very successful for epistemic reasoning in planning tasks. In this logic, the agent's knowledge is captured by modal epistemic operators whereas the system…
Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed, using an abstract…
The paper presents an approach to semantic grounding of language models (LMs) that conceptualizes the LM as a conditional model generating text given a desired semantic message formalized as a set of entity-relationship triples. It embeds…
Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…
Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Expressive querying of machine learning models - viewed as a form of intentional data - enables their verification and interpretation using declarative languages, thereby making learned representations of data more accessible. Motivated by…
Logic programs under the stable model semantics, or answer-set programs, provide an expressive rule-based knowledge representation framework, featuring a formal, declarative and well-understood semantics. However, handling the evolution of…
This paper presents AutoEval, a novel benchmark for scaling Large Language Model (LLM) assessment in formal tasks with clear notions of correctness, such as truth maintenance in translation and logical reasoning. AutoEval is the first…
Without explicit feedback, humans can rapidly learn the meaning of words. Children can acquire a new word after just a few passive exposures, a process known as fast mapping. This word learning capability is believed to be the most…