Pebble weighted automata and transitive - LSV
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
Reasoning about Complex Actions with Incomplete Knowledge: A
... state transitions, through the accessibility relation of Kripke structures. We introduce an action theory on the line of [6,18,19], in which actions are represented by modalities, and we extend it by allowing sensing actions as well as complex actions definitions. Our starting point is the modal logi ...
... state transitions, through the accessibility relation of Kripke structures. We introduce an action theory on the line of [6,18,19], in which actions are represented by modalities, and we extend it by allowing sensing actions as well as complex actions definitions. Our starting point is the modal logi ...
Sample Questions for Test 2
... The following practice problems are for Math 1200 Term test 2-Section E. To use them well, solve the problems, then discuss and compare your methods and answers. See if you can identify what particular knowledge and skills were required. 1. Prove that if 5x + 12 is even then x must be even. 2. Prove ...
... The following practice problems are for Math 1200 Term test 2-Section E. To use them well, solve the problems, then discuss and compare your methods and answers. See if you can identify what particular knowledge and skills were required. 1. Prove that if 5x + 12 is even then x must be even. 2. Prove ...
Beyond Quantifier-Free Interpolation in Extensions of Presburger
... arithmetic), denoted QPA. Combined with uninterpreted predicates (UP) and uninterpreted functions (UF), this allows us to encode the theory of extensional arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly fro ...
... arithmetic), denoted QPA. Combined with uninterpreted predicates (UP) and uninterpreted functions (UF), this allows us to encode the theory of extensional arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly fro ...
Notes on Modal Logic - Stanford University
... literature, typically ‘O’ is used instead of ‘2’ and ‘P ’ instead of ‘3’. • Epistemic Reading: 2ϕ means ‘ϕ is known’ and 3ϕ means ‘ϕ is consistent with the current information’. In this literature, typically ‘K’ is used instead of ‘2’ and ‘L’ instead of ‘3’. • Temporal Reading: 2ϕ means ‘ϕ will alwa ...
... literature, typically ‘O’ is used instead of ‘2’ and ‘P ’ instead of ‘3’. • Epistemic Reading: 2ϕ means ‘ϕ is known’ and 3ϕ means ‘ϕ is consistent with the current information’. In this literature, typically ‘K’ is used instead of ‘2’ and ‘L’ instead of ‘3’. • Temporal Reading: 2ϕ means ‘ϕ will alwa ...
Dealing with imperfect information in Strategy Logic
... fragment SL[1G] (One-Goal Strategy Logic) is strictly more expressive than ATL∗ , but not computationally more expensive [17]. However, despite its great expressiveness, there is one fundamental feature of most real-life situations that SL lacks, which is imperfect information. An agent has imperfec ...
... fragment SL[1G] (One-Goal Strategy Logic) is strictly more expressive than ATL∗ , but not computationally more expensive [17]. However, despite its great expressiveness, there is one fundamental feature of most real-life situations that SL lacks, which is imperfect information. An agent has imperfec ...
Modal Logic for Artificial Intelligence
... is valid, regardless of the sentences we use in the place of A and B. The only items that need to be fixed are ‘or’ and ‘not’ in this case. If we would replace ‘not’ by ‘maybe’, then the argument would not be valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . the ...
... is valid, regardless of the sentences we use in the place of A and B. The only items that need to be fixed are ‘or’ and ‘not’ in this case. If we would replace ‘not’ by ‘maybe’, then the argument would not be valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . the ...
Many-Valued Logic
... It is normal in the sense that it agrees with two-valued logic on the values assigned all combinations of 1s and 0s, and it is uniform in the sense that it maintains that, in defining the connectives, if a compound has the same value whether a component is true or false, it also has that value if th ...
... It is normal in the sense that it agrees with two-valued logic on the values assigned all combinations of 1s and 0s, and it is uniform in the sense that it maintains that, in defining the connectives, if a compound has the same value whether a component is true or false, it also has that value if th ...
AN EARLY HISTORY OF MATHEMATICAL LOGIC AND
... between logic and set theory. These two strains met at different points throughout the nineteenth century. This thesis will be about these meetings, and will ultimately argue that the history of such meetings is older than historians have previously thought. This story begins with the logic that cam ...
... between logic and set theory. These two strains met at different points throughout the nineteenth century. This thesis will be about these meetings, and will ultimately argue that the history of such meetings is older than historians have previously thought. This story begins with the logic that cam ...
Bilattices and the Semantics of Logic Programming
... here. Van Emden has proposed using real numbers in [0, 1] as quantitative truth values [20]. How should such a truth value space be modified if programs are distributed? Similar issues arise for any choice of truth value space, of course. M. Ginsberg has invented the elegant notion of bilattice ([14 ...
... here. Van Emden has proposed using real numbers in [0, 1] as quantitative truth values [20]. How should such a truth value space be modified if programs are distributed? Similar issues arise for any choice of truth value space, of course. M. Ginsberg has invented the elegant notion of bilattice ([14 ...
Modal Consequence Relations
... of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation between sets of formulae and a single formula. A consequence relation ` specifies which arguments are valid; the argument ...
... of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation between sets of formulae and a single formula. A consequence relation ` specifies which arguments are valid; the argument ...
Counterfactuals
... Comparing strict conditionals in this manner gives rise to an intuitive conception of what a counterfactual conditional is: a strict conditional with a very particular sphere of accessibility; in particular that φ ψ is true if and only if all worlds sufficiently similar to the base world make φ → ...
... Comparing strict conditionals in this manner gives rise to an intuitive conception of what a counterfactual conditional is: a strict conditional with a very particular sphere of accessibility; in particular that φ ψ is true if and only if all worlds sufficiently similar to the base world make φ → ...
vmcai - of Philipp Ruemmer
... as integer arithmetic with uninterpreted predicates, often generate interpolants with quantifiers, which makes subsequent calls to decision procedures involving these interpolants expensive. This is not by accident. In fact, in this paper we first show that interpolation of QPA+UP in general require ...
... as integer arithmetic with uninterpreted predicates, often generate interpolants with quantifiers, which makes subsequent calls to decision procedures involving these interpolants expensive. This is not by accident. In fact, in this paper we first show that interpolation of QPA+UP in general require ...
A LOGICAL SEMANTICS FOR NONMONOTONIC SORTS
... by any children of the template. Note that the division into "strict" and "default" for Bouma is only local to the template. At the next level in the hierarchy, what was strict becomes default. Thus "defaultness" is not a property of the information itself, as it is with NSs, but rather a relation o ...
... by any children of the template. Note that the division into "strict" and "default" for Bouma is only local to the template. At the next level in the hierarchy, what was strict becomes default. Thus "defaultness" is not a property of the information itself, as it is with NSs, but rather a relation o ...
Reductio ad Absurdum Argumentation in Normal Logic
... define, in several ways, the meaning, the semantics of a Logic Program. Several semantics were defined, some 2-valued, some 3-valued, and even multi-valued semantics. The current standard 2-valued semantics for Normal Logic Programs— the Stable Models Semantics [11] — has been around for almost 20 y ...
... define, in several ways, the meaning, the semantics of a Logic Program. Several semantics were defined, some 2-valued, some 3-valued, and even multi-valued semantics. The current standard 2-valued semantics for Normal Logic Programs— the Stable Models Semantics [11] — has been around for almost 20 y ...
Topological aspects of real-valued logic
... includes both applications of topological ideas to obtain results in pure model theory, and a modeltheoretic approach to the study of compacta via their rings of continuous functions viewed as metric structures. We introduce an infinitary real-valued extension of first-order continuous logic for met ...
... includes both applications of topological ideas to obtain results in pure model theory, and a modeltheoretic approach to the study of compacta via their rings of continuous functions viewed as metric structures. We introduce an infinitary real-valued extension of first-order continuous logic for met ...
logic for computer science - Institute for Computing and Information
... correspondingly different conventions of notation and rigour. To keep the within reasonable bounds we have decided to omit some of the lengthier explanations and proofs found in traditional logic texts in favour of introducing topics considered more ‘advanced’, that are central to modern computer sc ...
... correspondingly different conventions of notation and rigour. To keep the within reasonable bounds we have decided to omit some of the lengthier explanations and proofs found in traditional logic texts in favour of introducing topics considered more ‘advanced’, that are central to modern computer sc ...
Chapter 2 Propositional Logic
... then ∼P is also a wff. Second, clause ii) says that if we already have two wffs, then we can put an → between them, enclose the whole thing in parentheses, and we get another wff. (The resulting wff is often called a “conditional”, whose “antecedent” is the wff before the → and whose “consequent” is ...
... then ∼P is also a wff. Second, clause ii) says that if we already have two wffs, then we can put an → between them, enclose the whole thing in parentheses, and we get another wff. (The resulting wff is often called a “conditional”, whose “antecedent” is the wff before the → and whose “consequent” is ...
071 Embeddings
... For technical explanation of this term see Monk [1976] chapters 13 to 16, and Tarski, Mostowski and Robinson ...
... For technical explanation of this term see Monk [1976] chapters 13 to 16, and Tarski, Mostowski and Robinson ...
Logic Part II: Intuitionistic Logic and Natural Deduction
... 2. This proof contains of a proof of a. 3. It also contains a proof of b . 4. So if we take the proof of b and put it together with the proof of a, we obtain a proof of b ...
... 2. This proof contains of a proof of a. 3. It also contains a proof of b . 4. So if we take the proof of b and put it together with the proof of a, we obtain a proof of b ...
Classical Propositional Logic
... We can also ask whether individual sentences are truths of logic, contradictions, or contingent statements that give real information about the world. ...
... We can also ask whether individual sentences are truths of logic, contradictions, or contingent statements that give real information about the world. ...
Relevant and Substructural Logics
... collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define consequence relations within the confines of a Hilbert system, so here is where ...
... collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define consequence relations within the confines of a Hilbert system, so here is where ...
pdf
... apparition of some controversial results in analysis [37], mathematicians and logicians became interested in a more precise formalisation of Mathematics. Frege [66, 37] was the first to set the solid foundations for logic. He, among other things, presented a formalisation of the concept of function. ...
... apparition of some controversial results in analysis [37], mathematicians and logicians became interested in a more precise formalisation of Mathematics. Frege [66, 37] was the first to set the solid foundations for logic. He, among other things, presented a formalisation of the concept of function. ...
One-dimensional Fragment of First-order Logic
... two-variable logic were proved to be NEXPTIME-complete in [8]. The extension of two-variable logic with counting quantifiers, FOC2 , was shown decidable in [9], [15]. It was subsequently proved to be NEXPTIME-complete in [16]. Research concerning decidability of variants of two-variable logic has be ...
... two-variable logic were proved to be NEXPTIME-complete in [8]. The extension of two-variable logic with counting quantifiers, FOC2 , was shown decidable in [9], [15]. It was subsequently proved to be NEXPTIME-complete in [16]. Research concerning decidability of variants of two-variable logic has be ...
X - UOW
... Strictly speaking, as we don’t know what x or y are, in parts (ix) and (x), these should not be statements. In Mathematics, x and y usually represent real numbers and we will assume this is the case here. Therefore, (ix) is either true or false (even if we don’t know which) and (x) is always true, ...
... Strictly speaking, as we don’t know what x or y are, in parts (ix) and (x), these should not be statements. In Mathematics, x and y usually represent real numbers and we will assume this is the case here. Therefore, (ix) is either true or false (even if we don’t know which) and (x) is always true, ...
Jesús Mosterín
Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.