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Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Are intelligent machines really intelligent? Is the underlying philosophical concept of intelligence satisfactory for describing how the present systems work? Is understanding a necessary and sufficient condition for intelligence? If a…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
Neural algorithmic reasoning aims to capture computations with neural networks by training models to imitate the execution of classical algorithms. While common architectures are expressive enough to contain the correct model in the weight…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
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…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
The work concerns automatic generation of logical specifications from requirements models. Logical specifications obtained in such a way can be subjected to formal verification using deductive reasoning. Formal verification concerns…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
In response to a concern raised by Horty, this paper develops a two-tiered, preference-based semantic framework for modeling defeasible conditional obligations. The paper extends a Hansson-Lewis style preference semantics for dyadic deontic…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
We present a comprehensive approach to the automated formalization of legal texts using large language models (LLMs), targeting their transformation into Defeasible Deontic Logic (DDL). Our method employs a structured pipeline that segments…
This paper motivates the study of decision theory as necessary for aligning smarter-than-human artificial systems with human interests. We discuss the shortcomings of two standard formulations of decision theory, and demonstrate that they…
Making sense of incomplete and conflicting narrative knowledge in the presence of abnormalities, unobservable processes, and other real world considerations is a challenge and crucial requirement for cognitive robotics systems. An added…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…
Autonomous software agents operating in dynamic environments need to constantly reason about actions in pursuit of their goals, while taking into consideration norms which might be imposed on those actions. Normative practical reasoning…
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…
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…