Related papers: Around finite second-order coherence spaces
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
We explore a kind of first-order predicate logic with intended semantics in the reals. Compared to other approaches in the literature, we work predominantly in the multiplicative reals $[0,\infty]$, showing they support three generations of…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
To develop a full abstract denotational model of a process language based on prebisimulation preorder, its behavioural semantics has two problems: (1) Two processes related by a standard denotational interpretation afford the same finite…
A core problem in learning semantic parsers from denotations is picking out consistent logical forms--those that yield the correct denotation--from a combinatorially large space. To control the search space, previous work relied on…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…
We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi$ (in $\mathcal{L}_{\omega,\omega}$) is…
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…
The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
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…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…