Related papers: Induction and Recursion Principles in a Higher-Ord…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the linear-time/branching-time…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
This paper studies temporal planning in probabilistic environments, modeled as labeled Markov decision processes (MDPs), with user preferences over multiple temporal goals. Existing works reflect such preferences as a prioritized list of…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…