Related papers: Nominal semantics for predicate logic: algebras, s…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
A systematic way of defining variants of a modeling language is useful for adopting the language to domain or project specific needs. Variants can be obtained by adopting the syntax or semantics of the language. In this paper, we take a…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…
Disentangling the explanatory factors in complex data is a promising approach for generalizable and data-efficient representation learning. While a variety of quantitative metrics for learning and evaluating disentangled representations…
Nominalistic Logic (NL) is a new presentation of Paul Gilmore's Intensional Type Theory (ITT) as a sequent calculus together with a succinct nominalization axiom (N) that permits names of predicates as individuals in certain cases. The…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm,…
Although some work has been done on the metamathematics of Metamath, there has not been a clear definition of a model for a Metamath formal system. We define the collection of models of an arbitrary Metamath formal system, both for…
We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…
We present in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ with general TBoxes by using categorical language. In this setting, $\mathcal{ALC}$ concepts are represented as…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Motivated by considerations in the foundations of quantum mechanics and inspired by the literature on vague predicates, we introduce the concept of an opaque predicate. While in the case of vague predicates there is a kind of indeterminacy…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…