Related papers: Representing First-Order Causal Theories by Logic …
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
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…
Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
To resolve conflicts among norms, various nonmonotonic formalisms can be used to perform prioritized normative reasoning. Meanwhile, formal argumentation provides a way to represent nonmonotonic logics. In this paper, we propose a…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
In the last decades much research effort has been devoted to extending the success of model checking from the traditional field of finite state machines and various versions of temporal logics to suitable subclasses of context-free…
In recent years the search for a proper formal definition of actual causation -- i.e., the relation of cause-effect as it is instantiated in specific observations, rather than general causal relations -- has taken on impressive proportions.…
Recently, C-Log was introduced as a language for modelling causal processes. Its formal semantics has been defined together with introductory examples, but the study of this language is far from finished. In this paper, we compare C-Log to…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage…
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is a FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides…