Related papers: Proving Infinitary Formulas
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets. We explain how to interpret in this model the fixpoint…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…
We prove a Model Existence Theorem for a fully infinitary logic for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson and…