Related papers: Logical Predicates in Higher-Order Mathematical Op…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
We show a model construction for a system of higher-order illative combinatory logic $\mathcal{I}_\omega$, thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
We study an extension of \g propositional logic whose corresponding algebra is an ordered Abelian group. Then we expand the ideas to first-order case of this logic.
We suggest an ordering for the predicates in continuous logic so that the semantics of continuous logic can be formulated as a hyperdoctrine. We show that this hyperdoctrine can be embedded into the hyperdoctrine of subobjects of a suitable…