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In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…

We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…

First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…

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…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…

In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (LFI) a more appealing formalism for reasoning under uncertainty, it is important to develop…

Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…

A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…

In a previous paper we have presented a CEGAR approach for the verification of parameterized systems with an arbitrary number of processes organized in an array or a ring. The technique is based on the iterative computation of parameterized…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…

The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…

Reflecting our experiences in areas, like Algebraic Specifications, Abstract Model Theory, Graph Transformations, and Model Driven Software Engineering (MDSE), we present a general, category independent approach to Logics of First-Order…

Formal verification of variant requirements has gained much interest in the software product line (SPL) community. Feature diagrams are widely used to model product line variants. However, there is a lack of precisely defined formal…

Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…