Related papers: First-order answer set programming as constructive…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…
Justification logic is a term used to identify a relatively new family of modal-like logics. There is an established literature about propositional justification logic, but incursions on the first-order case are scarce. In this paper we…
We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…
The predominant challenge in weakly supervised semantic parsing is that of spurious programs that evaluate to correct answers for the wrong reasons. Prior work uses elaborate search strategies to mitigate the prevalence of spurious…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
Most of contemporary software systems are implemented using an object-oriented approach. Modeling phases -- during which software engineers analyze requirements to the future system using some modeling language -- are an important part of…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
We show that the existence of a first-order formula separating two monadic second order formulas over countable ordinal words is decidable. This extends the work of Henckell and Almeida on finite words, and of Place and Zeitoun on…
Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers)…
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
The fixed-template constraint satisfaction problem (CSP) can be seen as the problem of deciding whether a given primitive positive first-order sentence is true in a fixed structure (also called model). We study a class of problems that…
We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n),…
We present a logical system CFP (Concurrent Fixed Point Logic) from whose proofs one can extract nondeterministic and concurrent programs that are provably total and correct with respect to the proven formula. CFP is an intuitionistic…
This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback.…
An interval-valued fuzzy answer set programming paradigm is proposed for nonmonotonic reasoning with vague and uncertain information. The set of sub-intervals of $[0,1]$ is considered as truth-space. The intervals are ordered using…
Formal ontologies are axiomatizations in a logic-based formalism. The development of formal ontologies, and their important role in the Semantic Web area, is generating considerable research on the use of automated reasoning techniques and…
Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic…
We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The…