Related papers: Comonadic semantics for hybrid logic and bounded f…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
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…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Game comonads have brought forth a new approach to studying finite model theory categorically. By representing model comparison games semantically as comonads, they allow important logical and combinatorial properties to be exressed in…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…