Related papers: Complete First-Order Game Logic
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
The formal semantics of an interpreted first-order logic (FOL) statement can be given in Tarskian Semantics or a basically equivalent Game Semantics. The latter maps the statement and the interpretation into a two-player semantic game. Many…
In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance,…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of…
In this paper, we introduce game-theoretic semantics (GTS) for Qualitative Choice Logic (QCL), which, in order to express preferences, extends classical propositional logic with an additional connective called ordered disjunction. Firstly,…
Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…
Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional…
We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the…
This paper involves generalizing the Goldblatt-Thomason and the Lindstr\"om characterization theorems to first-order modal logic.
This article shows that there exist two particular linear orders such that first-order logic with these two linear orders has the same expressive power as first-order logic with the Bit-predicate FO(Bit). As a corollary we obtain that there…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties.…
First-order multiplicative intuitionistic linear logic (MILL1) can be seen as an extension of the Lambek calculus. In addition to the fragment of MILL1 which corresponds to the Lambek calculus (of Moot & Piazza 2001), I will show fragments…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of…
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a…