Related papers: Coinduction in Uniform: Foundations for Corecursiv…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…
This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
Proof search in non-confluent tableau calculi, such as the connection tableau calculus, suffers from excess backtracking, but simple restrictions on backtracking are incomplete. We adopt constraint learning to reduce backtracking in the…
Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity…
We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative…
It is well known that many-sorted logic can be reduced to unsorted first-order logic by adding predicates for each sort, relativizing quantifiers to these predicates, and adding appropriate axioms governing their behavior. Existing…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…
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…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
Non-wellfounded proof theory results from allowing proofs of infinite height in proof theory. To guarantee that there is no vicious infinite reasoning, it is usual to add a constraint to the possible infinite paths appearing in a proof.…