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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…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
We address the problem of belief revision of logic programs, i.e., how to incorporate to a logic program P a new logic program Q. Based on the structure of SE interpretations, Delgrande et al. adapted the well-known AGM framework to logic…
We carry out a semantic study of the constructive modal logic CK. We provide a categorical duality linking the algebraic and birelational semantics of the logic. We then use this to prove Sahlqvist style correspondence and completeness…
We introduce a new translation from linear temporal logic (LTL) to deterministic Emerson-Lei automata, which are omega-automata with a Muller acceptance condition symbolically expressed as a Boolean formula. The richer acceptance condition…
The multiplicative fragment of Linear Logic is the formal system in this family with the best understood proof theory, and the categorical models which best capture this theory are the fully complete ones. We demonstrate how the Hyland-Tan…
We show that current open-source foundational LLMs possess instruction capability and German legal background knowledge that is sufficient for some legal analysis in an educational context. However, model capability breaks down in very…
This paper studies a first-order expansion of a combination C+J of intuitionistic and classical propositional logic, which was studied by Humberstone (1979) and del Cerro and Herzig (1996), from a proof-theoretic viewpoint. While C+J has…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward L\"owenheim-Skolem property from classical model theory. We call this property as the…
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
It is shown that propositional calculuses of both quantum and classical logics are non-categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled by a weakly orthomodular lattice and that classical logic…
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…
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
LP$^{\supset,\mathsf{F}}$ is a three-valued paraconsistent propositional logic which is essentially the same as J3. It has most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic.…
In this note we contribute to the recently developing study of "almost Boolean" quantum logics (i.e. to the study of orthomodular partially ordered sets that are naturally endowed with a symmetric difference). We call them enriched quantum…